| 45. Apply integration to the expansion 00 =E(-1)"x" = 1- x+x – x +.. 1+x n=0 to prove that for -1

Q: 7.)C) f dx 3. X'e 0 8.

A: Given, ∫0∞x3e-2xdx

Q: 7. Find the area between f(x)=-x² + 4x and g(x) = x² - 6x +5 over the interval 0≤x≤1 Ei..

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Q: Match the integrals from negative infinity to time twith their corresponding functions that are zero…

A: Given graph of the functions 1. 2.

Q: b 1+ e2x Evaluate the integral. ex xp 1 + e2x

A: Given that: ∫01ex1+e2xdx

Q: Q3. Use Romberg integration to compute R33 for the following integral. 1.6 2x dx x² -1

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Q: (b) Determine whether the following integrals converge. (i) ² x²+x-1 x5 + 3x dx, /2 5²1² ln(1+x²) x…

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Q: Suppose that, given g(x), you need to prove convergence of accompanying integral via limit…

A: Solution for 1: given ∫012sinπx2x32(1-x2)dx, g(x)=1x Let  f(x)=sinπx2x32(1-x2) So…

Q: 8. Determine the number M and the interval width h so that the composite trapezoidal rule for M…

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Q: +00 dx d.x (1+x)/x

A: Given: To show: The given integral converges.

Q: 1. ſ (x-1)dx x2+5x+6

A: The given integration is ∫(x-1)x2+5x+6 dx  We have to find the integration for the given integral

Q: 5 Evaluate the definite integral f(x) dx given the following: -3 f(x) = for x 2

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Q: Find the area of the region bounded by e21.2.png f(x) = = a/4 + 3x – x² and the x -axis using Left…

A: Left riemann sum  ∫ab  f(x)dx≈Δxf(x0)+f(x1)++f(x2)+....+f(xn-1)+f(xn)

Q: If In y = 3 sinh x show that dy (a) (1+r2)()² = 9y², dx (b) (1+ x²)- dy da? dy +x- – 9y = 0. da…

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Q: You found that the reduction formula of a certain integral is In = x"+2e2= - (n + 2) In-1 and that 1…

A: As per our guidelins we can solve only 1 question. The next question can be reposted.  Here we have…

Q: 11:33 dx The improper integral xVIn x converges to 2 the above diverges to -∞ the above

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Q: Determine whether or not the infinite series below converges.

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Q: 13)Evaluate 13 Evaluate the integral s 5x--Xt27 dx x (x²+G) -1 3 tan 3+C b)(-ト2フx)、1mlxCx?ss)1c Sx3…

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Q: 1. Write the following improper integral as a limit. x-3x In(x)-1 dx x (x-1)

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Q: 2º" (n!)" for n = 0,1, 2, .... (0! (2n+1)! xn for n = 1, 2,... .) (Hint: Start by showing that if In…

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Q: .\o x³ + 1 43-48 Use the Comparison Theorem to determine whether the integral is convergent or…

A: As per our guidelines we can solve only three sub parts at a time. Please repost unsolved part…

Q: 1. Write the note on geometrical interpretation of integration and also state why addition of…

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Q: I don't understant this hw problem

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Q: Write the definite integral for the Riemann sum: 2 (5 + 2)* + (5+ x 2)* + (5 + × 3)*+...+(5 + x n)"|…

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Q: 169 dx Evaluate the integral 8 x( In x) 13

A: As per our company guidelines we are supposed to answer only first question. Kindly post other…

Q: 10 dt Use trigonometric substitution to evaluate t2 Vt2 – 25 O V3/50- O v3/72. O In(7+4v3). This…

A: Given integral is Firstly, we will find the following indefinite integral  We will use the…

Q: What is the area beneath the curve y=x2 +1 and above the x-axis from x = 0 to x = 4 by using the…

A: Here we have to use Riemann right end sum

Q: 3. Evaluate the integral of the following functions extended over the interval indicated for each by…

A: Since there are multiple questions the first one is answered as per our guidelines.Kindly repost if…

Q: What is the integral of x" cos ax dx ? хN sin ax А. -=S nx"-1 sin ax dx + а а хN sin ax B. n -"Sxn-1…

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Q: -2 Evaluate the definite integral S: 1 dx. 1 x+a²

A: general answer is Ln|(2+a^2)÷(1+a^2)| Where a = -3/5 Final answer is Ln|59/34|

Q: Evaluate the following integral using the pezo laSimpson's rules with n = 10 In (x² +1)e °0** dx.…

A: Simpson's rule of approximation is as follows: ∫abf(x) dx≈∆x3fx0+4fx1+2fx2+4fx3+...+fxnwhere ∆x=b-an…

Q: Evaluate the following improper integrals whenever they are convergent. а. 1 b. (2.x+3)* 00 1 :dx V1…

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Q: An improper integral e-X dx Converges if : O A.r1 OCr0

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Q: 7 So Suppose f(x)dx = 6, f(x)dx =5, and g(x)dx = 8. Evaluate the following integrals. 2 2

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Q: Steb by step

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Q: Q3. Evaluate the following Integrals S cot³ x csc3x dx x3-x²-8x-1 • Express in partial fractions.…

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Q: 2. Find the values of p for which the integral converges and evaluate the integral for th dx a) dx…

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Q: 6. Examine the convergence of the following improper integrals: a) So de x+1 Vx4-x 8. 1 b) xVx2 -4 1…

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Q: 3. Evaluate the integral of the following functions extended over the interval indicated for each by…

A: Note: There are multiple questions. Few questions has multiple subparts. No specific question has…

Q: Evaluate the indefinite integral as an infinite series. cos(x) – 1 dx + C n = 1

A: sol: Given ∫ cos x-1x              consider  cos x-1x = -1x+ cos xx…

Q: Find the indefinite integral. dm O 27 hm-9- 3m+C O-27 hlm-S+3m+C O 27 rim-S+ 3m +C O27 In/m-9+3m+C O…

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Q: Evaluate the following indefinite integral by using Partial Fraction (3x – 1) dx x2 – 4x + 3 O 4…

A: First we factorize the denominator of the integrand .Then we use the partial fraction method to…

Q: Find any value of c for which the improper integral cx + 36 x2 + 1 9. da x (4 x + 5) converges.

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Q: 2. S (x+1)dx x²(x-1)

A: We can find the answer in the following steps.

Q: Use the first four terms of the taylor expansion about x = 0 to sin x*) estimate the following…

A: According to the given information, it is required to use the first four terms of taylor series to…

Q: Q2)For what value(s) of k does the integral converge : -o kx 1 x²+1 dx 2x Then evaluate the…

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Q: 2. Evaluate the following improper integrals if convergent, otherwise justify why the integral…

A: We have to evaluate the following improper integrals if convergent, or justify why the integral…

Q: 1. Let p be constant, and consider the improper integral 1 d.x x (In(x))" /2 For what values of p…

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Q: Q5: Compute by part the following indefinite integral Sx. In x dx

A: Given  that a integration and we solve it by part. We know that integration of Xn  is -  = Xn+1/n+1.…