Calculus (MindTap Course List)
Calculus (MindTap Course List)
8th Edition
ISBN: 9781285740621
Author: James Stewart
Publisher: Cengage Learning
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Differential Equations
Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…
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Chapter 7.8, Problem 68E

As we saw in Section 6.5, a radioactive substance decays exponentially: The mass at time t is m ( t ) = m ( 0 ) e k t , where m(0) is the initial mass and k is a negative constant.

The mean life M of an atom in the substance is

M = − k ∫ 0 ∞ t e k t d t

For the radioactive carbon isotope, C 14 , used in radiocarbon dating, the value of k is − 0.000121 . Find the mean life of a C 14 atom.

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Chapter 7 Solutions

Calculus (MindTap Course List)

Ch. 7.1 - Evaluate the integral using integration by parts...Ch. 7.1 - Evaluate the integral using integration by parts...Ch. 7.1 - Evaluate the integral. xcos5xdxCh. 7.1 - Evaluate the integral. ye0.2ydyCh. 7.1 - Evaluate the integral. te3tdtCh. 7.1 - Prob. 6ECh. 7.1 - Evaluate the integral. (x2+2x)cosxdxCh. 7.1 - Evaluate the integral. t2sintdtCh. 7.1 - Evaluate the integral. cos1xdxCh. 7.1 - Prob. 10E
Ch. 7.1 - Evaluate the integral. t4lntdtCh. 7.1 - Prob. 12ECh. 7.1 - Evaluate the integral. tcsc2tdtCh. 7.1 - Prob. 14ECh. 7.1 - Evaluate the integral. (lnx)2dxCh. 7.1 - Evaluate the integral. z10zdzCh. 7.1 - Evaluate the integral. e2sin3dCh. 7.1 - Prob. 18ECh. 7.1 - Evaluate the integral. z3ezdzCh. 7.1 - Prob. 20ECh. 7.1 - Evaluate the integral. xe2x(1+2x)2dxCh. 7.1 - Prob. 22ECh. 7.1 - Evaluate the integral. 01/2xcosxxdxCh. 7.1 - Prob. 24ECh. 7.1 - Evaluate the integral. 02ysinhydyCh. 7.1 - Evaluate the integral. 12w2lnwdwCh. 7.1 - Evaluate the integral. 15lnRR2dRCh. 7.1 - Prob. 28ECh. 7.1 - Evaluate the integral. 0xsinxcosxdxCh. 7.1 - Evaluate the integral. 13arctan(1/x)dxCh. 7.1 - Prob. 31ECh. 7.1 - Prob. 32ECh. 7.1 - Prob. 33ECh. 7.1 - Prob. 34ECh. 7.1 - Evaluate the integral. 12x4(lnx)2dxCh. 7.1 - Prob. 36ECh. 7.1 - Prob. 37ECh. 7.1 - Prob. 38ECh. 7.1 - Prob. 39ECh. 7.1 - Prob. 40ECh. 7.1 - Prob. 41ECh. 7.1 - Prob. 42ECh. 7.1 - Evaluate the indefinite integral. Illustrate, and...Ch. 7.1 - Prob. 44ECh. 7.1 - Prob. 45ECh. 7.1 - Prob. 46ECh. 7.1 - Prob. 47ECh. 7.1 - a Prove the reduction formula...Ch. 7.1 - a Use the reduction formula in Example 6 to show...Ch. 7.1 - Prove that, for even powers of sine,...Ch. 7.1 - Use integration by parts to prove the reduction...Ch. 7.1 - Prob. 52ECh. 7.1 - Use integration by parts to prove the reduction...Ch. 7.1 - Prob. 54ECh. 7.1 - Prob. 55ECh. 7.1 - Use Exercise 52 to find x4exdx.Ch. 7.1 - Prob. 57ECh. 7.1 - Prob. 58ECh. 7.1 - Prob. 59ECh. 7.1 - Prob. 60ECh. 7.1 - Prob. 61ECh. 7.1 - Prob. 62ECh. 7.1 - Use the method of cylindrical shells to find the...Ch. 7.1 - Prob. 64ECh. 7.1 - Calculate the volume generated by rotating the...Ch. 7.1 - Calculate the average value of f(x)=xsec2x on the...Ch. 7.1 - The Fresnel function S(x)=0xsin(12t2)dt was...Ch. 7.1 - A rocket accelerates by burning its onboard fuel,...Ch. 7.1 - A particle that moves along a straight line has...Ch. 7.1 - Prob. 70ECh. 7.1 - Suppose that f(1)=2,f(4)=7,f(1)=5,f(4)=3, and f is...Ch. 7.1 - Prob. 72ECh. 7.1 - We arrived at Formula 5.3.2, V=ab2xf(x)dx, by...Ch. 7.1 - Let In=0/2sinnxdx. a Show that I2n+2I2n+1I2n. b...Ch. 7.2 - Evaluate the integral. sin2xcos3xdxCh. 7.2 - Prob. 2ECh. 7.2 - Prob. 3ECh. 7.2 - Prob. 4ECh. 7.2 - Evaluate the integral. sin5(2t)cos2(2t)dtCh. 7.2 - Evaluate the integral. tcos5(t2)dtCh. 7.2 - Prob. 7ECh. 7.2 - Prob. 8ECh. 7.2 - Evaluate the integral. 0cos4(2t)dtCh. 7.2 - Prob. 10ECh. 7.2 - Prob. 11ECh. 7.2 - Prob. 12ECh. 7.2 - Evaluate the integral. cossin3dCh. 7.2 - Evaluate the integral. sin2(1/t)t2dtCh. 7.2 - Prob. 15ECh. 7.2 - Prob. 16ECh. 7.2 - Evaluate the integral. sin2xsin2xdxCh. 7.2 - Evaluate the integral. sinxcos(12x)dxCh. 7.2 - Prob. 19ECh. 7.2 - Prob. 20ECh. 7.2 - Evaluate the integral. tanxsec3xdxCh. 7.2 - Prob. 22ECh. 7.2 - Prob. 23ECh. 7.2 - Prob. 24ECh. 7.2 - Evaluate the integral. tan4xsec6xdxCh. 7.2 - Prob. 26ECh. 7.2 - Prob. 27ECh. 7.2 - Evaluate the integral. tan5xsec3xdxCh. 7.2 - Evaluate the integral. tan3xsec6xdxCh. 7.2 - Prob. 30ECh. 7.2 - Prob. 31ECh. 7.2 - Prob. 32ECh. 7.2 - Evaluate the integral. xsecxtanxdxCh. 7.2 - Prob. 34ECh. 7.2 - Prob. 35ECh. 7.2 - Evaluate the integral. /4/2cot3xdxCh. 7.2 - Prob. 37ECh. 7.2 - Prob. 38ECh. 7.2 - Prob. 39ECh. 7.2 - Evaluate the integral. /6/3csc3xdxCh. 7.2 - Prob. 41ECh. 7.2 - Prob. 42ECh. 7.2 - Prob. 43ECh. 7.2 - Prob. 44ECh. 7.2 - Prob. 45ECh. 7.2 - Prob. 46ECh. 7.2 - Prob. 47ECh. 7.2 - Prob. 48ECh. 7.2 - Prob. 49ECh. 7.2 - If 0/4tan6xsecxdx=I, express the value of...Ch. 7.2 - Prob. 51ECh. 7.2 - Prob. 52ECh. 7.2 - Prob. 53ECh. 7.2 - Prob. 54ECh. 7.2 - Prob. 55ECh. 7.2 - Evaluate sinxcosxdx by four methods: a the...Ch. 7.2 - Find the area of the region bounded by the given...Ch. 7.2 - Find the area of the region bounded by the given...Ch. 7.2 - Prob. 59ECh. 7.2 - Prob. 60ECh. 7.2 - Prob. 61ECh. 7.2 - Prob. 62ECh. 7.2 - Prob. 63ECh. 7.2 - Prob. 64ECh. 7.2 - A particle moves on a straight line with velocity...Ch. 7.2 - Prob. 66ECh. 7.2 - Prob. 67ECh. 7.2 - Prove the formula, where m and n are positive...Ch. 7.2 - Prob. 69ECh. 7.2 - A finite Fourier series is given by the sum...Ch. 7.3 - Evaluate the integral using the indicated...Ch. 7.3 - Prob. 2ECh. 7.3 - Prob. 3ECh. 7.3 - Prob. 4ECh. 7.3 - Evaluate the integral. x21x4dxCh. 7.3 - Prob. 6ECh. 7.3 - Evaluate the integral. 0adx(a2+x2)3/2a0Ch. 7.3 - Evaluate the integral. dtt2t216Ch. 7.3 - Evaluate the integral. 23dx(x21)3/2Ch. 7.3 - Prob. 10ECh. 7.3 - Evaluate the integral. 01/2x14x2dxCh. 7.3 - Evaluate the integral. 02dt4+t2Ch. 7.3 - Evaluate the integral. x29x3dxCh. 7.3 - Prob. 14ECh. 7.3 - Evaluate the integral. 0ax2a2x2dxCh. 7.3 - Prob. 16ECh. 7.3 - Evaluate the integral. xx27dxCh. 7.3 - Prob. 18ECh. 7.3 - Evaluate the integral. 1+x2xdxCh. 7.3 - Prob. 20ECh. 7.3 - Evaluate the integral. 00.6x2925x2dxCh. 7.3 - Prob. 22ECh. 7.3 - Evaluate the integral. dxx2+2x+5Ch. 7.3 - Prob. 24ECh. 7.3 - Evaluate the integral. x23+2xx2dxCh. 7.3 - Prob. 26ECh. 7.3 - Prob. 27ECh. 7.3 - Prob. 28ECh. 7.3 - Evaluate the integral. x1x4dxCh. 7.3 - Prob. 30ECh. 7.3 - Prob. 31ECh. 7.3 - Prob. 32ECh. 7.3 - Find the average value of f(x)=x21/x,1x7.Ch. 7.3 - Find the area of the region bounded by the...Ch. 7.3 - Prob. 35ECh. 7.3 - Prob. 36ECh. 7.3 - Find the volume of the solid obtained by rotating...Ch. 7.3 - Find the volume of the solid obtained by rotating...Ch. 7.3 - Prob. 39ECh. 7.3 - The parabola y=12x2 divides the disk x2+y28 into...Ch. 7.3 - Prob. 41ECh. 7.3 - Prob. 42ECh. 7.3 - Find the area of the crescent-shaped region called...Ch. 7.3 - A water storage tank has the shape of a cylinder...Ch. 7.4 - Write out the form of the partial fraction...Ch. 7.4 - Prob. 2ECh. 7.4 - Write out the form of the partial fraction...Ch. 7.4 - Prob. 4ECh. 7.4 - Write out the form of the partial fraction...Ch. 7.4 - Prob. 6ECh. 7.4 - Evaluate the integral. x4x1dxCh. 7.4 - Prob. 8ECh. 7.4 - Evaluate the integral. 5x+1(2x+1)(x1)dxCh. 7.4 - Prob. 10ECh. 7.4 - Evaluate the integral. 0122x2+3x+1dxCh. 7.4 - Prob. 12ECh. 7.4 - Prob. 13ECh. 7.4 - Prob. 14ECh. 7.4 - Prob. 15ECh. 7.4 - Evaluate the integral. 12x2+4x2+x1x3+x2dxCh. 7.4 - Prob. 17ECh. 7.4 - Prob. 18ECh. 7.4 - Evaluate the integral. 01x2+x+1(x+1)2(x+2)dxCh. 7.4 - Prob. 20ECh. 7.4 - Evaluate the integral. dt(t21)2Ch. 7.4 - Prob. 22ECh. 7.4 - Evaluate the integral. 10(x1)(x2+9)dxCh. 7.4 - Prob. 24ECh. 7.4 - Evaluate the integral. 4xx3+x2+x+1dxCh. 7.4 - Prob. 26ECh. 7.4 - Evaluate the integral. x3+4x+3x4+5x2+4dxCh. 7.4 - Prob. 28ECh. 7.4 - Evaluate the integral. x+4x2+2x+5dxCh. 7.4 - Prob. 30ECh. 7.4 - Evaluate the integral. 1x31dxCh. 7.4 - Prob. 32ECh. 7.4 - Evaluate the integral. 01x3+2xx4+4x2+3dxCh. 7.4 - Prob. 34ECh. 7.4 - Prob. 35ECh. 7.4 - Prob. 36ECh. 7.4 - Evaluate the integral. x23x+7(x24x+6)2dxCh. 7.4 - Prob. 38ECh. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Prob. 40ECh. 7.4 - Prob. 41ECh. 7.4 - Prob. 42ECh. 7.4 - Prob. 43ECh. 7.4 - Prob. 44ECh. 7.4 - Prob. 45ECh. 7.4 - Prob. 46ECh. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Prob. 48ECh. 7.4 - Prob. 49ECh. 7.4 - Prob. 50ECh. 7.4 - Prob. 51ECh. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Prob. 53ECh. 7.4 - Prob. 54ECh. 7.4 - Prob. 55ECh. 7.4 - Prob. 56ECh. 7.4 - Prob. 57ECh. 7.4 - Prob. 58ECh. 7.4 - The German mathematician Karl Weierstrass 18151897...Ch. 7.4 - Use the substitution in Exercise 59 to transform...Ch. 7.4 - Prob. 61ECh. 7.4 - Prob. 62ECh. 7.4 - Prob. 63ECh. 7.4 - Prob. 64ECh. 7.4 - Prob. 65ECh. 7.4 - Prob. 66ECh. 7.4 - One method of slowing the growth of an insect...Ch. 7.4 - Factor x4+1 as a difference of squares by first...Ch. 7.4 - Prob. 69ECh. 7.4 - Prob. 70ECh. 7.4 - The rational number 227 has been used as an...Ch. 7.4 - Prob. 72ECh. 7.4 - Prob. 73ECh. 7.4 - Prob. 74ECh. 7.4 - Prob. 75ECh. 7.5 - Evaluate the integral. cosx1sinxdxCh. 7.5 - Prob. 2ECh. 7.5 - Evaluate the integral. 14ylnydyCh. 7.5 - Prob. 4ECh. 7.5 - Prob. 5ECh. 7.5 - Prob. 6ECh. 7.5 - Prob. 7ECh. 7.5 - Evaluate the integral. tsintcostdtCh. 7.5 - Prob. 9ECh. 7.5 - Evaluate the integral. cos(1/x)x3dxCh. 7.5 - Prob. 11ECh. 7.5 - Prob. 12ECh. 7.5 - Evaluate the integral. sin5tcos4tdtCh. 7.5 - Prob. 14ECh. 7.5 - Evaluate the integral. xsecxtanxdxCh. 7.5 - Prob. 16ECh. 7.5 - Prob. 17ECh. 7.5 - Prob. 18ECh. 7.5 - Prob. 19ECh. 7.5 - Evaluate the integral. e2dxCh. 7.5 - Prob. 21ECh. 7.5 - Prob. 22ECh. 7.5 - Prob. 23ECh. 7.5 - Prob. 24ECh. 7.5 - Prob. 25ECh. 7.5 - Prob. 26ECh. 7.5 - Evaluate the integral. dx1+exCh. 7.5 - Prob. 28ECh. 7.5 - Prob. 29ECh. 7.5 - Prob. 30ECh. 7.5 - Prob. 31ECh. 7.5 - Prob. 32ECh. 7.5 - Prob. 33ECh. 7.5 - Prob. 34ECh. 7.5 - Prob. 35ECh. 7.5 - Prob. 36ECh. 7.5 - Prob. 37ECh. 7.5 - Prob. 38ECh. 7.5 - Prob. 39ECh. 7.5 - Prob. 40ECh. 7.5 - Prob. 41ECh. 7.5 - Prob. 42ECh. 7.5 - Prob. 43ECh. 7.5 - Prob. 44ECh. 7.5 - Evaluate the integral. x5ex3dxCh. 7.5 - Prob. 46ECh. 7.5 - Prob. 47ECh. 7.5 - Prob. 48ECh. 7.5 - Prob. 49ECh. 7.5 - Prob. 50ECh. 7.5 - Prob. 51ECh. 7.5 - Prob. 52ECh. 7.5 - Prob. 53ECh. 7.5 - Prob. 54ECh. 7.5 - Prob. 55ECh. 7.5 - Prob. 56ECh. 7.5 - Prob. 57ECh. 7.5 - Prob. 58ECh. 7.5 - Prob. 59ECh. 7.5 - Prob. 60ECh. 7.5 - Prob. 61ECh. 7.5 - Prob. 62ECh. 7.5 - Prob. 63ECh. 7.5 - Prob. 64ECh. 7.5 - Prob. 65ECh. 7.5 - Evaluate the integral. /4/3ln(tanx)sinxcosxdxCh. 7.5 - Prob. 67ECh. 7.5 - Prob. 68ECh. 7.5 - Prob. 69ECh. 7.5 - Prob. 70ECh. 7.5 - Prob. 71ECh. 7.5 - Prob. 72ECh. 7.5 - Prob. 73ECh. 7.5 - Prob. 74ECh. 7.5 - Prob. 75ECh. 7.5 - Prob. 76ECh. 7.5 - Prob. 77ECh. 7.5 - Prob. 78ECh. 7.5 - 7.5 EXERCISES Evaluate the integral. xsin2xcosxdxCh. 7.5 - Prob. 80ECh. 7.5 - Prob. 81ECh. 7.5 - Prob. 82ECh. 7.5 - Prob. 83ECh. 7.5 - Prob. 84ECh. 7.6 - Prob. 1ECh. 7.6 - Prob. 2ECh. 7.6 - Use the indicated entry in the Table of Integrals...Ch. 7.6 - Prob. 4ECh. 7.6 - Prob. 5ECh. 7.6 - Prob. 6ECh. 7.6 - Prob. 7ECh. 7.6 - Prob. 8ECh. 7.6 - Prob. 9ECh. 7.6 - Prob. 10ECh. 7.6 - Prob. 11ECh. 7.6 - Prob. 12ECh. 7.6 - Prob. 13ECh. 7.6 - Prob. 14ECh. 7.6 - Prob. 15ECh. 7.6 - Prob. 16ECh. 7.6 - Prob. 17ECh. 7.6 - Prob. 18ECh. 7.6 - Prob. 19ECh. 7.6 - Use the Table of Integrals on Reference Pages 610...Ch. 7.6 - Prob. 21ECh. 7.6 - Prob. 22ECh. 7.6 - Prob. 23ECh. 7.6 - Prob. 24ECh. 7.6 - Prob. 25ECh. 7.6 - Prob. 26ECh. 7.6 - Prob. 27ECh. 7.6 - Prob. 28ECh. 7.6 - Prob. 29ECh. 7.6 - Prob. 30ECh. 7.6 - Prob. 31ECh. 7.6 - Prob. 32ECh. 7.6 - Prob. 33ECh. 7.6 - Prob. 34ECh. 7.6 - Verify Formula 53 in the Table of Integrals a by...Ch. 7.6 - Prob. 36ECh. 7.6 - Prob. 37ECh. 7.6 - Prob. 38ECh. 7.6 - Prob. 39ECh. 7.6 - Prob. 40ECh. 7.6 - Prob. 41ECh. 7.6 - Prob. 42ECh. 7.6 - Prob. 43ECh. 7.6 - Use a computer algebra system to evaluate the...Ch. 7.6 - Prob. 45ECh. 7.6 - Prob. 46ECh. 7.7 - Let I=04f(x)dx, where f is the function whose...Ch. 7.7 - Prob. 2ECh. 7.7 - Prob. 3ECh. 7.7 - Draw the graph of f(x)=sin(12x2) in the viewing...Ch. 7.7 - Use a the Midpoint Rule and b Simpsons Rule to...Ch. 7.7 - Use a the Midpoint Rule and b Simpsons Rule to...Ch. 7.7 - Prob. 7ECh. 7.7 - Prob. 8ECh. 7.7 - Prob. 9ECh. 7.7 - Use a the Trapezoidal Rule, b the Midpoint Rule,...Ch. 7.7 - Prob. 11ECh. 7.7 - Prob. 12ECh. 7.7 - Prob. 13ECh. 7.7 - Prob. 14ECh. 7.7 - Prob. 15ECh. 7.7 - Prob. 16ECh. 7.7 - Use a the Trapezoidal Rule, b the Midpoint Rule,...Ch. 7.7 - Prob. 18ECh. 7.7 - a Find the approximations T8 and M8 for the...Ch. 7.7 - a Find the approximations T10 and M10 for...Ch. 7.7 - Prob. 21ECh. 7.7 - How large should n be to guarantee that the...Ch. 7.7 - Prob. 23ECh. 7.7 - Repeat Exercise 23 for the integral 114x3dx. The...Ch. 7.7 - Find the approximations Ln, Rn, Tn and Mn for n=5,...Ch. 7.7 - Find the approximations Ln, Rn, Tn and Mn for n=5,...Ch. 7.7 - Prob. 27ECh. 7.7 - Find the approximations Tn, Mn, and Sn for n=6 and...Ch. 7.7 - Estimate the area under the graph in the figure by...Ch. 7.7 - The widths in meters of a kidney-shaped swimming...Ch. 7.7 - a Use the Midpoint Rule and the given data to...Ch. 7.7 - a A table of values of a function g is given. Use...Ch. 7.7 - Prob. 33ECh. 7.7 - A radar gun was used to record the speed of a...Ch. 7.7 - Prob. 35ECh. 7.7 - Water leaked from a tank at a rate of rt liters...Ch. 7.7 - The table supplied by San Diego Gas and Electric...Ch. 7.7 - Prob. 38ECh. 7.7 - Use Simpsons Rule with n=8 to estimate the volume...Ch. 7.7 - Prob. 40ECh. 7.7 - Prob. 41ECh. 7.7 - The figure shows a pendulum with length L that...Ch. 7.7 - The intensity of light with wavelength traveling...Ch. 7.7 - Prob. 44ECh. 7.7 - Sketch the graph of a continuous function on 0, 2...Ch. 7.7 - Sketch the graph of a continuous function on 0, 2...Ch. 7.7 - Prob. 47ECh. 7.7 - Prob. 48ECh. 7.7 - Prob. 49ECh. 7.7 - Prob. 50ECh. 7.8 - Explain why each of the following integrals is...Ch. 7.8 - Prob. 2ECh. 7.8 - Prob. 3ECh. 7.8 - Prob. 4ECh. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Prob. 6ECh. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Prob. 8ECh. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Prob. 40ECh. 7.8 - Prob. 41ECh. 7.8 - Prob. 42ECh. 7.8 - Prob. 43ECh. 7.8 - Prob. 44ECh. 7.8 - Prob. 45ECh. 7.8 - Sketch the region and find its area if the area is...Ch. 7.8 - Prob. 47ECh. 7.8 - Prob. 48ECh. 7.8 - Use the Comparison Theorem to determine whether...Ch. 7.8 - Use the Comparison Theorem to determine whether...Ch. 7.8 - Use the Comparison Theorem to determine whether...Ch. 7.8 - Use the Comparison Theorem to determine whether...Ch. 7.8 - Use the Comparison Theorem to determine whether...Ch. 7.8 - Use the Comparison Theorem to determine whether...Ch. 7.8 - Prob. 55ECh. 7.8 - Prob. 56ECh. 7.8 - Prob. 57ECh. 7.8 - Prob. 58ECh. 7.8 - Find the values of p for which the integral...Ch. 7.8 - a Evaluate the integral 0xnexdx for n = 0, 1, 2,...Ch. 7.8 - Prob. 61ECh. 7.8 - Prob. 62ECh. 7.8 - Prob. 63ECh. 7.8 - Prob. 64ECh. 7.8 - Prob. 65ECh. 7.8 - Astronomers use a technique called stellar...Ch. 7.8 - Prob. 67ECh. 7.8 - As we saw in Section 6.5, a radioactive substance...Ch. 7.8 - In a study of the spread of illicit drug use from...Ch. 7.8 - Prob. 70ECh. 7.8 - Prob. 71ECh. 7.8 - Prob. 72ECh. 7.8 - If f(t) is continuous for t0, the Laplace...Ch. 7.8 - Prob. 74ECh. 7.8 - Prob. 75ECh. 7.8 - Prob. 76ECh. 7.8 - Prob. 77ECh. 7.8 - Prob. 78ECh. 7.8 - Prob. 79ECh. 7.8 - Find the value of the constant C for which the...Ch. 7.8 - Prob. 81ECh. 7.8 - Prob. 82ECh. 7.R - Prob. 1CCCh. 7.R - Prob. 2CCCh. 7.R - Prob. 3CCCh. 7.R - Prob. 4CCCh. 7.R - Prob. 5CCCh. 7.R - Prob. 6CCCh. 7.R - Prob. 7CCCh. 7.R - Prob. 8CCCh. 7.R - Prob. 1TFQCh. 7.R - Prob. 2TFQCh. 7.R - Prob. 3TFQCh. 7.R - Prob. 4TFQCh. 7.R - Prob. 5TFQCh. 7.R - Prob. 6TFQCh. 7.R - Prob. 7TFQCh. 7.R - Determine whether the statement is true or false....Ch. 7.R - Determine whether the statement is true or false....Ch. 7.R - Determine whether the statement is true or false....Ch. 7.R - Determine whether the statement is true or false....Ch. 7.R - Prob. 12TFQCh. 7.R - Prob. 13TFQCh. 7.R - Prob. 14TFQCh. 7.R - Prob. 1ECh. 7.R - Prob. 2ECh. 7.R - Prob. 3ECh. 7.R - Prob. 4ECh. 7.R - Prob. 5ECh. 7.R - Prob. 6ECh. 7.R - Prob. 7ECh. 7.R - Prob. 8ECh. 7.R - Prob. 9ECh. 7.R - Prob. 10ECh. 7.R - Prob. 11ECh. 7.R - Prob. 12ECh. 7.R - Prob. 13ECh. 7.R - Prob. 14ECh. 7.R - Prob. 15ECh. 7.R - Prob. 16ECh. 7.R - Prob. 17ECh. 7.R - Prob. 18ECh. 7.R - Prob. 19ECh. 7.R - Prob. 20ECh. 7.R - Prob. 21ECh. 7.R - Prob. 22ECh. 7.R - Prob. 23ECh. 7.R - Evaluate the integral. excosxdxCh. 7.R - Prob. 25ECh. 7.R - Prob. 26ECh. 7.R - Prob. 27ECh. 7.R - Prob. 28ECh. 7.R - Prob. 29ECh. 7.R - Prob. 30ECh. 7.R - Prob. 31ECh. 7.R - Prob. 32ECh. 7.R - Prob. 33ECh. 7.R - Prob. 34ECh. 7.R - Prob. 35ECh. 7.R - Prob. 36ECh. 7.R - Prob. 37ECh. 7.R - Prob. 38ECh. 7.R - Prob. 39ECh. 7.R - Prob. 40ECh. 7.R - Evaluate the integral or show that it is...Ch. 7.R - Prob. 42ECh. 7.R - Prob. 43ECh. 7.R - Prob. 44ECh. 7.R - Evaluate the integral or show that it is...Ch. 7.R - Evaluate the integral or show that it is...Ch. 7.R - Evaluate the integral or show that it is...Ch. 7.R - Evaluate the integral or show that it is...Ch. 7.R - Evaluate the integral or show that it is...Ch. 7.R - Prob. 50ECh. 7.R - Prob. 51ECh. 7.R - Prob. 52ECh. 7.R - Prob. 53ECh. 7.R - Prob. 54ECh. 7.R - Prob. 55ECh. 7.R - Prob. 56ECh. 7.R - Prob. 57ECh. 7.R - Prob. 58ECh. 7.R - Verify Formula 33 in the Table of Integrals a by...Ch. 7.R - Prob. 60ECh. 7.R - Prob. 61ECh. 7.R - Prob. 62ECh. 7.R - Prob. 63ECh. 7.R - Use a the Trapezoidal Rule, b the Midpoint Rule,...Ch. 7.R - Prob. 65ECh. 7.R - Prob. 66ECh. 7.R - The speedometer reading v on a car was observed at...Ch. 7.R - Prob. 68ECh. 7.R - Prob. 69ECh. 7.R - Prob. 70ECh. 7.R - Use the Comparison Theorem to determine whether...Ch. 7.R - Find the area of the region bounded by the...Ch. 7.R - Prob. 73ECh. 7.R - Prob. 74ECh. 7.R - Prob. 75ECh. 7.R - Prob. 76ECh. 7.R - Prob. 77ECh. 7.R - Prob. 78ECh. 7.R - Prob. 79ECh. 7.R - Prob. 80ECh. 7.P - Three mathematics students have ordered a 14-inch...Ch. 7.P - Evaluate 1x7xdx The straightforward approach would...Ch. 7.P - Prob. 3PCh. 7.P - Prob. 4PCh. 7.P - Prob. 5PCh. 7.P - A man initially standing at the point O walks...Ch. 7.P - Prob. 7PCh. 7.P - If n is a positive integer, prove that...Ch. 7.P - Prob. 9PCh. 7.P - Prob. 10PCh. 7.P - If 0ab, find limt0{01[bx+a(1x)]tdx}1/tCh. 7.P - Graph f(x)=sin(ex) and use the graph to estimate...Ch. 7.P - Prob. 13PCh. 7.P - Prob. 14PCh. 7.P - Prob. 15PCh. 7.P - A rocket is fired straight up, burning fuel at the...
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