70. Use the fact that (b*) = (In b) b* to prove that (ek*) = dx dx kekx. ||

Q: integral (In x) 3  dx

A:

Q: .find integrals by using Beta fun dx (1-x*) ーズ

A: Using the Beta function, it can be written as follows.

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

A:

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: 4. Evaluate the integral. S tan (2x) sec°(2x) dx

A:

Q: 5.Use trapezoidal rule to evaluate f,(x² + 1)7 dx by taking n = 4.

A:

Q: Use Simpson's rule with n = 4 to approximate cos(x) dx 1

A:

Q: Obtain a-(In x)? dx.

A: Given,  ∫x-5(lnx)2dx

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: Evaluate thl integraus in H3) dx (44) dx dx 17 +x? 45

A: Disclaimer:  Since you have posted multiple questions, I will answer first three questions. If you…

Q: Find the indefinite integral ∫tan3 3x dx

A:

Q: Evaluate the integral.  integral  sec 2 x  tan  3 x  dx

A: Consider the following integral:

Q: What is the integral of x2(2-x)^(1/3) dx on the interval [1,2]?

A:

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

A:

Q: S(歳)dx 2

A:

Q: 8. Evaluate x dx from the definition of RS-integral.

A:

Q: Use integration by parts to prove the reductionformula.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: 6. S sin (3x – 1) dx. cos Vi dx. 7. Evaluate th dx. Show yo 8. 3 dx. S (! + 1)(t – 1) dt. 9.

A:

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: Find upper and lower bounds for

A:

Q: Find indefinite integral.

A: ∫5lnz+3z dz Put, 5lnz+3=t⇒5·1z+0=dtdz⇒1zdz=dt5

Q: Evaluate the definite integral. ∫(lower bound=π/4)(upper bound=0)sin(4t)dt

A: Given,             ∫π40sin4tdt

Q: What is the integral of sin^5 x cos^3 x dx if the lower limit is zero and the upper limit is T/2?

A:

Q: Evaluate the integral S cos ³ x + 8 sin x cos³² x + 6s in ² x dx; cosx #0 2 cos²x

A:

Q: 4. Use the definition of integration to find (1+2x' ) dx , that is find lim f(x; )Ax

A:

Q: 7. To evaluate f-cos X-1 dx, the integrand can be transformed to? 1-sin? x

A: Follow the procedure given below.

Q: 33. Prove for a > 0: dx x2 + a 1 tan Ja

A:

Q: Explain why the improper integral (x + 3) sin(x) dx L. (x² + 1)(x² + 4)² is convergent. 8

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Q: can this be evalnated by using L'HUSpital's Rule? im x2 3x+ 2 sin(x x)

A:

Q: I Braluate th FOllowing integralis 3+cos (logqx) dx x sin (loga x )

A:

Q: Evaluate integral of interval ln 8, 0 of ex d x

A: We have to evaluate

Q: What is wrong with this calculation? 1 dx In |x||, = In 1 - In 1 = 0 - 1

A: The integral of 1xwith respect to x is log(|x|). where x≠0, cause if it is zero then function became…

Q: Match the integral expression on the left to an equal expression on the right. Ssin(3x)sin(4x)dx -…

A: Let's find.

Q: Evaluate ( Sech²(In x) dx

A: In this question we will use basic of calculus i.e concept of integration. First we will convert the…

Q: 9. Use Simpson's Rule to approximate the integral f Vx3 – 1 dx withn = 6.

A: We have to find the value of given integral using Simpson's rule.

Q: Evaluate the indefinite integral.

A: It is required to evaluate the indefinite integral:

Q: This is exercise 26 of Section 7.5 page 460. Find the integral æ* sin(æ²) dx-

A: Answer is given in the picture

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

A:

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: Compute the indefinite integral 2. - 4e²² + 6z – 5) 5) dx.

A: We know that integration of ex is ex . And integration of 1/x is lnx. Integration of xn is xn+1/…

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: