If In |(In x)" dx, show that In = x(In x)" – n.Ip-1- Hence find nx)* dx.

Q: Evaluate the integral 2x dx x – 6 ILO fer th

A: SOLUTION-

Q: Evaluate the definite integral S (1+ 2x) dx using Riemann sum.

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Q: 3 Estimate the integral 1 dx by the trapezoidal rule using n = 4. + 1 Vx3

A: ∫abf(x)dx≈Δx(f(x0)+f(x1)2+f(x1)+f(x2)2+f(x2)+f(x3)2+⋯+ f(xn−1)+f(xn)2) where ∆x =b -an

Q: Determine whether the improper integral diverges or converges. dx 1. (2х-1)3 dx 2. x +1

A: No.2 The improper integral is of second kind where f(x) = 1/(x+1) has one point of infinte…

Q: 6. The improper integral dx converges to /x- 5 '5 Vr-5

A: The given integral is an improper integral of second kind.

Q: Evaluate the improper intergal 1 dx using the residue (x² + 100)? theorem.

A: The given problem is to evaluate the given improper integral using the residue theorem. We have to…

Q: 3 2 dx . 3

A:

Q: 12)Use the Trapezoidal Rule to estimate the integral ₁√x² - 1 dx using 4 intervals. Round to the…

A: Solve the following

Q: Determine whether the improper integral diverges or converges. dx 1.So (2x-1) 7 dx 2. x +1

A: We have to determine whether the improper integral ∫-17 dxx+1 diverges or converges.

Q: Evaluate the improper integral: e-X dx

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Evaluate the improper integral, 5 if exists : dx (5 – x)3

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Q: Show that (In kx) dx (In x), where x > 0 and k is a positive dx real number.

A: ddxln kx=ddxln x, where x>0 & k is a positive real number.

Q: If the integral diverges, indicate that using the checkbox. 6 dx The integral diverges x(x + 1)

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Q: O Use a linear approxi mation (differential) to estimate 3999

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Q: Use trapezoidal with 3 level romberg (k=3) to evaluate the integral from lower limit 0 to upper…

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Q: 3. Evaluate the improper integral: dx | Tale + 1)'

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Q: Determine whether the improper integral diverges or converges. 1 dx e2x + e-2x

A: Evaluate integral,

Q: Evaluate the integral.

A: Given: ∫ex1-e2xdx

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

A:

Q: What is the integral of sin^5 x dx if the lower limit is O and the upper limit is T/2?

A: We have to find out

Q: Evaluate A Se-* dx by Simpson's 1/3 rule with n=10, work for six digit

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Q: Evaluate the integral. S. 4 x* - 3 dx 14 4 x* - 3 dx = 14

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Q: 3 Estimate the integral 1 dx by Simpson's rule using n= 8. Vx3 + 5

A: Given that a integration and ask estimate value use Simpson rule when n= 8. In Simpson rule we can…

Q: Compute integral below with the use of substitution. eð 1 -dx x In° x

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Q: Evaluate the integral. 4 3* dx /3

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Q: Determine the indefinite integral 6+8x3 dx by algebraic manipulation. Assume x>0 when In (x)…

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

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

A: We have to find

Q: Evaluate the integral. 5x In(x) dx:

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Q: evaluate using the appropriate method or combination of methods.

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Q: find integral by Beta function -x?)ž dx O otherwise 3 VE

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Q: /tangent slupe rosin (20) when dy ス 5. 555 653 3. not of thc above

A: Topic:- application of derivatives in polar form

Q: How do I do this one?

A: Given integral is The integral is improper and can be evaluated as follows

Q: In the indefinite Integral Sin(cosh x + ex)- A In(cosh x + e*) B sinh x + ex C In(cosh x + e*)- sinh…

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Q: e2x +2e* -dx e* +1 2.

A:

Q: Evaluate the integral.

A: Given: The integral, ∫12x5lnx dx.

Q: Evaluate dx using Simpson's rule. 3

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Q: or show that it is divergent Evaluate the integral dx 10

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Q: Evaluate the integral. . 4 1) x In 2x dx 1

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Q: 7) Estimate the value of e dx using Simpson's rule using 8 subintervals.

A: Given: ∫02ex2dx Here, n = 8 subintervals

Q: Use Simpson’s Rule with n=4 to approximate the integral 8∫0√xdx.

A:

Q: 55. Show that dx J+4 converges by comparing with x³ + xdx. -3 dx. х

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Q: .find the integral by Gamma fun y(-Iny)5 dy

A: Gamma function is defined as Γ(x)=∫0∞xn-1e-x dx .               Disclaimer: Since you have asked…

Q: integral In x 2 dx

A:

Q: Find the indefinite integral. 8x In (5x)dx

A: The given indefinite integral is ∫8xln5xdx.

Q: Give the general antiderivative for the integrand in the definite integral (cos +1)dx. cos x

A: Simply integrate and put the limit than simplify.

Q: Evaluate the double integral. 5 25- х2 dy dx Jo

A: First, integrate with respect to y

Q: Evaluate the definite integral S (1 + 2x) dx using Riemann sum.

A:

Q: Determine the following indefinite integral. S ex 400-e2x dx, x> In 20

A: Given, ∫ex400-e2xdx