If a and b are positive constants, evaluate the following integrals: e -ax -bx (a) -dx;

Q: Given two functions, f1(x) = 2x and f2(x) = x2, explain what∫0^2 [f1(x)−f2(x)]dxrepresents and…

A: We have to calculate this definite integral which is given by

Q: /2 + x dx

A: The solution are next step

Q: Find the value of this Multiple Integral. ,(x² + 3xy²) dx dy

A: Here we have to evaluate I=∫02∫0yx2+3xy2dxdy

Q: Evaluate the integrals ∫ex sin (ex) dx

A:

Q: 2) Find each integral by substitution a) [5x*(x' +7)'dx b) [x'e' dx

A: a) ∫5x4x5+73dx......(1) Put x5+7=t Differentiate the above function ddxx5+7=dxt5x4dx=dt Substitute…

Q: Evaluate the integral. (Use C for the constant of integration.) x3 xp 49 + x2

A: In this we have to solve by putting the value of u=49+x^2 I'm providing hand written solution for…

Q: Evaluate the integral, ∫(5/(x√(1+(ln⁡x )^2 ) ) dx〗.

A:

Q: Take the integral from 0 to 2 of (x/x2+4x+8)dx

A:

Q: state what method applies and how one applies it, but do not evaluate the integral:

A:

Q: 1. L, 4x³ dx -2

A: Value of definite integral is 65.

Q: -(-3у?-у-2)dy 2y3+y2+4y

A:

Q: [(b) find the integral in the interval [1,4] S(3/2 sqrt(x)-4/x^2) dx ].

A: To evaluate the given integral on [1,4]

Q: Find the indetinite integral S(8x2-12x+7)dx

A: Given integral is By using the result of integration we get

Q: J (2x + 3)´dx

A: Given integral, ∫2x+32dx

Q: 00 1 dx x(Inx)2

A:

Q: x3 sin(x) dx

A: Solve by integration by parts

Q: Find the integral. (Use C for the constant of integration.) (x8 + 9-X) dx

A:

Q: Evaluate the integrals ∫ ln x/x4 dx

A: The given integral is, I=∫lnxx4dx Substitute, lnx=t ⇒1xdx=dtx=etx3=e3t Therefore, the integral…

Q: valuate the integral of x(x – 5)^12 dx from 5 to 6.

A: We have to find out

Q: x+3 dx x²+6x+7

A:

Q: Evaluate the integrals

A: 59. ∫0∞x2e-xdx60. ∫0∞xe3xdx

Q: 1 -dx х6—х

A: We have to evaluate the integral by substitution method: ∫1x6-xdx Rewriting the integral,…

Q: Evaluate the integrals ∫ 1/x6(x5 + 4) dx

A: Integration : ∫1x6(x5+4)dxWe need to perform partial fraction decomposition:

Q: Evaluate the integrals ∫ 1/x(x4 + 1) dx

A: Given: I=∫dxxx4+1 for evaluating given integral we take out x4 from bracket so,…

Q: 1 |xe*dx 1-

A:

Q: VIt VI dx тр. a.

A: According to our policy at Bartleby, I can solve only one question. Given an integral : I=∫1+xx dx…

Q: Use reduction formula to evaluate the given integral xe" dx

A:

Q: Find the integral by algebraic substitution: ∫dx/√1+4x

A: In some cases integrals can be simplified to standard integrals by using an appropriate…

Q: Evaluate the integrals. ∫x7√(x4 + 1) dx

A: The given integral is ∫x7x4+1dx.

Q: Evaluate the integral. (Use C for the constant of integration.) x + 21 dx x2 + 24x + 148

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: x19 In(x)dx 1

A:

Q: In(sin x) d.x 2

A: We need to find whether given integral is proper of improper.

Q: Evaluate the integrals So 2 log2 (x+2) dx (x+2)

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Q: (3x5 - 2x - 1) dz. dx

A:

Q: Evaluate the integral in terms of the constants.

A:

Q: First make a substitution and then use integration by parts to evaluate the integral. (Use C for the…

A: We have to find

Q: Evaulte the integral when x > 0 ln(x^2+17x+70)

A: Integrand, I = ln(x2+17x+70)x2+17x+70 can be factorised as shown below:x2+17x+70 = x2+10x + 7x+70 =…

Q: - y = [sec(x)]3z

A:

Q: Evaluate the integrals.∫(√x + 1)/√x dx

A: Given:∫x+1xdx

Q: Evaluate the integral. 3x Va? - x² dx

A:

Q: For which of the following integrals should substitution be used, instead of Integration by Parts?…

A: Solution :option D substituition be…

Q: 2. S", sec t dt -T/4

A:

Q: Evaluate the given integral with suitable substitution: (42x + 42) dz

A:

Q: Evaluate the integral. 5x2 Va? – x2 dx

A:

Q: Evaluate the integral. x+ 10 dx x+2

A:

Q: Evaluate the given integrals. 7x-4Vx 1. S S VE () dx

A: Let's find.

Q: x-1 x² + 5x + 8 S dx

A:

Q: 1 dx

A:

Q: Use the special or Bessel function to solve TWO from the following integrals In x 1. [ dx x* +1 2.…

A: It is given that

Q: Evaluate the integral.

A: Now consider,

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.