8. Which of the following is true for the integral dx XP(In x)ª e (a) It diverges for p < 1 and converges for p > 1. (b) It diverges forp<1 and converges for p > 1.

Q: 4. Evaluate the improper integral dx +e"

A: We know that, ddxex=ex ∫1a2+x2dx=1atan-1xa+c tan-1(1)=π4 tan-1(∞)=π2

Q: O: If the improper integral converges,Show and find its valuo or ex plain why it diverges: O. X Sin…

A: The integral will converge if it is equal to some finite fixed value.

Q: 7. Evaluate the Integral S (x + 3) dx

A:

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

A:

Q: 6. Evaluate the integral ex e* +e-xdx

A:

Q: 3. 'Evaluate the integral. 5 dx х0.2

A:

Q: dr

A: Given integration is : ∫x2-9x3dx To find the value of integration.

Q: '1 1 Given that x² dx = use this fact and the properties of integrals to evaluate (8 — бх2) dx.

A:

Q: For which values of the lower limit of integration a is the following integral convergent. 1 dx 4x…

A: Here the limits of the integral are finite. So, the integral will be convergent if its value is a…

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

A:

Q: To apply the integral test for 3n2 + 1 n3 +n n=1 we evaluate the improper integral 0 3x2 + 1 dx. x3…

A: Solve the following

Q: 19. Evaluate the integral Z √(x^2 − 9) / x^3 dx

A: firstly divide the numerator by denominator part by part to simplify the integration

Q: 6. The improper integral 1 dx converges to Vx-5 4 2 попе 1

A:

Q: 3. Evaluate the double integral /sin(x+y) dx dy by using Simpson's 1/3-rule with four sub-intervals.

A: I = ∫0π2∫0π2sin x+ydxdy,

Q: ∞ e4y dy

A:

Q: 7. Which of these is a non-elementary integral? In(2y² + 1) А. -dy 4y e-x cosh(2x) В. c. [ e-x +…

A: Non-elementary integral for a given elementary function is an  indefinite integral that is, itself,…

Q: 3. Does the improper integral 2 dx converge? et +e-*

A:

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

A:

Q: The improper integral e-3x dx 0. equals Refer: improper integral O 1 O 1/3

A:

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

A:

Q: So S(x + 3) dy dx 3. Evaluate the double integral:

A:

Q: Evaluate the integral: e³+ cosh2x33+ cosh2xsinh2x dx A (3e)3+ sinh2x 2+In3 +C (3e)3+cosh2x B) 2+2ln3…

A:

Q: 2 Evaluate the improper integral e2a dx, if exists.

A: Evaluate the improper integral  ∫-∞2 e2x dx

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

A:

Q: 4. Evaluate the following integral by first reversing the order of integration dx dy.

A:

Q: Evaluate the integrals that converge: 3 dx 2x ! b) | a) dx (x² + 5)³ 3 – x -00

A:

Q: 6. The improper integral 1 dx converges to х -5 попe 2 1 4

A: We have to find

Q: 1 The improper integral -dx is given by: x² +8x+41 Select one: O a. None of these sec-'((b+4)/5) de…

A:

Q: 2. Find the integral of xe*dx using Simpson's 1/3 Rule with n = 4.

A: Simpson's 1/3 rule for integration :-  here 'h' is difference between each interval which are…

Q: 3 4-3x S²³ So dx dy

A: To evaluate the given double integral.∫03∫04-3x dx dy

Q: e2x 2.) S. dx ex – 5

A:

Q: 4-Évaluate the following integrals a) In dx b) ] ()"- dx 5/2 tan x

A: Integration:   The collection of all antiderivatives of f is called indefinite integral of f with…

Q: 3. Apply Romberg quadrature to •1 1 dx 1+ x2 for h = 1, 1/2, 1/4, 1/8. Show a table of approximate…

A: We are given the following definite integral : ∫1/(1+x2) dx from 0 to 1 And we have to solve it…

Q: 57 Evaluate the integral |[xy dy dx. 12

A:

Q: Calculate the integral approximation S6 for 0 -1 4-² dx.

A: In this question we have to find the Integration.

Q: 3 Evaluate the improper integral :S e2 dx

A: e-198

Q: 1. Evaluate the indefinite integral. Hint: U-substitution. 3 dx x In x

A: ∫ 3x lnx dx 3∫ 1lnx·1x dx

Q: 6. Evaluate the integral. x³e2x dx

A:

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

A:

Q: b. d. 1 dx x4 ° 1 dx f. | h. (y³ – 3y²) - 8

A:

Q: Calculate the integral approximation S12 for 1 dx. x²+1 S12 =

A:

Q: - Prove using integrals Proper tos : e even sin()fc) dx=0 -b 9- For even functions.

A:

Q: 1. Evaluate the integral: x/x – 1 dx.

A: answer = 1.0667   explanation is given in below step

Q: 2 Evaluate the improper integral 4x e dx, if exists. 8.

A: Given that,           ⇒           ∫-∞2e4x dx   ,   if exist             ⇒         find the…

Q: 1. Use the table of integrals to integrate the followin a) S sin ) s in () dt

A:

Q: Evaluate the integral: e3+ cosh2x33 + cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 +C B (3e)3+cosh2x 2+2ln3…

A: This question can be solved using integration by substitution.

Q: ormulas to compute the following antiderivative. x-1 x² -dx.

A:

Q: 3. Find the indefinite integral. S (3e* + +x³ + 3) dx

A:

Q: 2 Evaluate the improper integral e4z dx, if exists. a) The nature of the integral is:

A: Explanation of the solution is given below...

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…