5 Find a limit equal to In(2x – 1) dx.

Q: 10. Evaluate the integral. dx x²/4 – x²

A:

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

A:

Q: 4 18. Evaluate the indefinite integral / dx. 3 X,

A: Given integral to find ∫4x3dx To integrate this first take the constant out 4∫1x3dx Applying the…

Q: Find the limit of sin Ø/Ø as approaches 0°. * 00 1 -1 ООО

A: Using formula.

Q: 3. Evaluate the integral Sx cosx dx.

A: Please see the below picture for detailed solution.

Q: Lx In x dx.

A: ∫1exlnxdx

Q: (x2 + 2x) cos x dx

A: Given,         ∫x2+2xcosxdx

Q: 1 Evaluate the improper integral dx. (x – 3)3/2' 3 -

A:

Q: mcory amu LAampIOS 45. Finding an upper limit of an iterated integral Solve for a: 1-x² ¢4-x²-y 4 dz…

A:

Q: Evaluate the integral. S-3x cos(2x) dx

A:

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

A:

Q: Express lim,00 E= cos( + ) in integral notation. i=1 _2n

A: Since, the above equation is given in the form of Riemann's integral, which is given by-…

Q: П 9. In(1+ kx) sin r x(ekz – x – 1) lim \k=2

A:

Q: - Evaluate the integral dx using Simpson's th rule e* – 1 3 -

A:

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

A:

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

A:

Q: Use symmetry to evaluate the following integral. | (6- |x)) dx - 1

A: The given integral,     ∫-116-xdx

Q: Find the integral of 12 sin^5 x cos^5 x dx if the lower limit is O and the upper limit is T/2.

A:

Q: 1. Rewrite the following improper integrals as a limit and then evalute them, or state that they…

A:

Q: A) Evaluate the following integral dx (x - 1)(x-2)(x − 3) - , 10 points

A:

Q: 3. 6x° cos (x*) dx

A:

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: 2. Find the indefinite integral: S (Vã+ - x + - 1) dx 6 .3 X X

A:

Q: Evaluate the integral. S (x² + 8)e-x dx

A: We need to evaluate integral.

Q: Evaluate the integral √ (k+ 2) ( k + 3) dx

A: Note:- according to the company policy we can attempt only one question so please upload the next…

Q: 1. (a) Prove the following. | (In x)"dx = x(In x)" – n (In x)-' dx

A: To prove that 1.a. ∫lnxndx=xlnxn-n∫lnxn-1dxb. Using 1.a compute the following      ∫lnx3dx

Q: Evaluate the integral. 3y- cos xy dy dx x/3 O 5(1 - cos 3) O 3(1 - cos 3) O cos 3 -1 (1 cos 3)

A: Given: ∫03∫x313y2 cos xy dy dx We have x3≤y≤1 and 0≤x≤3 This can be seen as: We can change the…

Q: 2 3. Evaluate the integral ||x dx -2 O 2 4

A:

Q: d) Numerically approximate the integral 2+ cos(2Vx) dx by 3 Simpson's rule with 6 strips

A: Given integral is ∫022+cos2xdx. To evaluate the integral using Simpson's 38 rule. Consider the…

Q: 3. Prove that -2/3 dx diverges by showing that х lim -2/3 dx = 00 х

A: Given limit is Since one of the limit of integration is infinite , so we evaluate the limit as…

Q: - Using Greens date $(x2 + y)dx bounding of the 0<x<1 and x' sysx.

A:

Q: Evaluate the integral: square root of x cos(1+ x to the 3/2 power) dx

A: Evaluate the integral

Q: 3.12 Еxpress lim n00 n k3D cos 1+ as an integral. (Be sure to include the lower and upper limits|of…

A: Given: limn→∞ 2n∑k=1ncos1+2kn To convert this into the integral , use the following method

Q: on 1. Complete the following computation a' In(8x)dx via integration by parts f(x) = In(8x) and…

A:

Q: 15 Find the integral | 2/x (1+x) dx.

A:

Q: Show that integral 0 to infinity  x2 e -x2  dx = 1/2 integral 0 to infinity e -x2  dx

A:

Q: find the limit as x approaches 0. 12sin(3x)/1-cos(3x) = as x approaches 0

A:

Q: 1. Evaluate the definite integral S ,2 C (9x² + 5)dx by the limit definition.

A:

Q: 25 3. In r If the triple integral fo So So (xe") dydr dz Find the upper limit value E.

A: We have to find the value of E.

Q: if p> 1, (diverges; if p <1. 0o dx Prove that f p- 1 хР 1 Hence evaluate: dx. x6

A:

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

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

Q: Find a limit equal to (x2 – 8)dx. 3

A: The integral of some functions are given below. 1)∫x2dx=x33+c2)∫8dx=8x+c Use the above and find the…

Q: Evaluate the integral 3. 2х cos(xy)dydx 2

A:

Q: 2 1. Evaluate the integral: dx 2 x2-x

A:

Q: Find the indefinite integral ∫ [arctan(x/2)] / (4 + x2) dx

A: ∫arctanx24+x2dx Now put, arctanx2=t⇒11+x22·12=dtdx⇒11+x24·12=dtdx⇒44+x2·12=dtdx⇒24+x2=dtdx⇒14+x2…

Q: 13. Evaluate the integral dx x – 1

A:

Q: 3. Find the integral: L,x*dx

A:

Q: 12) a) Use either the Trapezoid OR Midpoint Rule to estimate [ In(1+e* ) dx using at least four…

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

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.