Q: Find the values of p for which each integral converges. 2 80 dx dx b. x(In x)P x(In x)P GELEH 2 dx…

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Q: (b) dx (1+ x²)² 0,

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Q: Given √ 1 pdx.c A (-∞,1] B (1,00⁰) Ⓒ (-∞0,00) D (0,1) dx, determine all value/values of P for which…

A: This can be solved as follows:

Q: 17. Find the values of p for which the integral So dx converges. OpE (-1,1) Op21 Op 1 Opsl

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Q: Starting with the given fact that the type 1 improper integral dx converges to p-1 1 when p>1, use…

A: Value of type-II improper integral

Q: How do I do this one?

A: First we write the integration with limit

Q: Solve the following integral using substitution method: X S. dx √x²-1

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Q: Find the values of p for which each integral converges. dx dx b. x(In x)P a. x(In x)P dx a. For what…

A: The integration is said to be converges when the improper integrals with limits occurs whereas when…

Q: 69. Find the values of p for which each integral converges. dx x(ln x)P dx b. a. x(ln x)P

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Q: For what value of c does the integral converge? Evaluate the integral for this value of c.

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Q: Determine whether the following integral converges or diverges. a) 6.00 ㅠ b) fo X (x² + 1)² tan x…

A: Let us determine whether the integral converges or diverges in the next steps.

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

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

Q: 1. Determine if the following improper integrals converges or diverges dx a. (1+r*)'/3 b. cos(x-1)…

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Q: Which of the following integrals converges? S а. 1+x 0.1 b. dx 1+x с. dx 1+x 01 dx 1+x0.1 d. е.…

A: We use the fact given in the image to identify the convergence of integral.      Ans-(a)

Q: 12. Determine the value of the following and classify if the integral is convergent or divergent. dx…

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Q: For what real numbers p does the improper integral epa dx converge? Find the value of the integral…

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Q: Use Gauss-Legendre formula to evaluate the integral e¯x*dx_with n = 3.

A: Evaluate the integral          ∫01ex2dx using Gauss-Legendre formula with n=3.

Q: The improper integral 1 dx converges to 5. x-5 0 4 o l o 2 none

A: From the given problem: I=∫591x-5dx...(1)   Use the substitution method to solve the given…

Q: Determine if the following improper integrals converge or diverge dx 2) 1 + e-2x -8

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Q: 4. Use the comparison property to calculate if the following integral converge: sin? a dx. V1+x3

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Q: evaluate the given integral.

A: we have to evaluate the given integral: ∫x2+5x-1x+4dx let the given integral be I. therefore,…

Q: 4. Use the comparison property to calculate if the following integral converge: sin? x dx. | 1+

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Q: The improper integral J dx converges to x-5 4 о попе 1

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Q: Use Simpson’s Rule with n= 10 to approximate the integral 0 to 1 e x2   dx

A: Given: n=10I=∫01ex2dx

Q: Does the following integral converge or diverge? Show all steps 1 (x – 1)4/3 dx

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Q: For what value of a, b > 0 is the following integral convergent. dx . x°(1+x³)

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Q: 1. Find the values of the following improper integrals with unbounded domains of integration, if…

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Q: Which of the following integrals is convergent? Select the correct answers. .24 0 of OP 0 2 X dx dx…

A: We have to find which of the following integral is convergent. (a).…

Q: evaluate the given integral.

A: Solution:-The given integral is  ∫x+2(x-1)(x+3)dx since  x+2(x-1)(x+3) is solved by partial…

Q: Which two of the following integrals converge? dx а. 1+cos x xdx b. sin xln (cos x) dx с. d. 1+x…

A: For a) ∫0πdx1+cosx=∫0π12sec2x2dx=tanx20π=∞ Hence divergence For b)…

Q: The following improper integral dx x2-9 diverges to -00 converges to – V15 This option This option…

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Q: Find the values of p for which each integral converges 2 dx а. x(In x}P 1 b. x(In x) 2 2 dx a. For…

A: (a) Given : ∫12dxx(lnx)p

Q: For the next three exercises, determine whether the integral converges or diverges. 1+ sin z S x² 3…

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Q: Find the values of p for which each integral converges. 2 dx xp b. x(In x)P a. x(In x)P 2 a. For…

A: Given problem:-

Q: The following improper integral dx x²-9 converges to –/15 diverges to -0 O This option O This option…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the indefinite integral

A: To evaluate: ∫2x+1ex2+xdx Let substitute t=x2+x dtdx=2x+1dt=2x+1dx Substituting the value,…

Q: 1 dx is convergent The integral x1.10

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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: 27. For what value or values of a does ах |dx 2x x² + 1 converge? Evaluate the corresponding…

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Q: [2'e'dx X

A: Given

Q: 1. State whether each of the following integrals converges or diverges: 00 (a) хЗdx (b) х3 dx -2/3…

A: Since we only answer up to three sub parts. We’ll answer the first three. Please resubmit the…

Q: Evaluate this integral I = ∫ a 0 x^2 √(a^2 - x^2)   dx. Then determine whether the statement is true…

A: Given integral is,

Q: For what values of  a is ∫0∞ eax cos x dx convergent? Evaluatethe integral for those values of a?

A: ∫0∞eaxcosx dx Now, ∫0∞eaxcosx dx=limt→∞∫0teaxcosx dx=limt→∞eaxa2+1acosx+sinx0t    ∵∫eaxcosbx…

Q: e ( + 4)2 dx = Evaluate the integral if it converges. Enter the exact answer, or enter na if it…

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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: Evaluate the integral. 6)e¯X dx

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Q: Find the following improper integrals and then state whether it converges or diverges. a) S," In…

A: The  improper integral is given as ∫1∞lnx2dx To find : whether the given  integral converges or…

Q: Which one of the four integrals below has a finite value ? Select one: 00 x? dx 00 1 dx 3 00 x dx 3…

A: We have to find the integral which have finite value.

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.