5. Compute the following integrals: (a) In x dx C y? +1

Q: Evaluate the integral, if it exists.  ∫01 y2 √(y3 + 1) dy

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Q: Evaluate the following integral.

A: Complete the square of 3 + 2x –x2:

Q: dz 2 t´ + Zz-3

A:

Q: b) Evaluate the integral by parts. S, x* Inx dx

A: given I= ∫1ex4 ln x dxby using LIATE rule we can rewrite integral as    I= ∫1e ln x   (x4) dx     =…

Q: (b) 'elz)x d: 1

A:

Q: - Evaluate the following integrals. 1 1. J x(9 – In² x}5/2 dx

A: To evaluate: ∫1x9-ln2x52dx Let, I = ∫1x9-ln2x52dx

Q: Evaluate the fo llowing integrals S Sin () dx

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Q: Evaluate the integrals in ∫2y dy/y2 - 25

A: Given integral:

Q: Evaluate the improper integrals: S xe-*dx (a) dx (b)

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Q: 3. Compute the following integrals. 2/5 (a) V4 – 25x² dx.

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Q: Evaluate the following integral.

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Q: 3. Calculate the following integrals: (a) So 43 dx. (b) S x5-° dr. 1 (c) J 1Te- dr.

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Q: 2х 3 2. Ver + 2 dx

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Q: Q1) Evaluate the following integral using By Parts Method: х.In(x3 + x) dx

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Q: : Determine the fool wing integrals: 2. S x² In(x + 4) dx

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Q: 24. Evaluate the integral: ," dy y2+2y-3

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Q: 2. Evaluate the following integrals. (a) Si S S*** xy dz dy dx

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Q: 6. Compute the following improper integrals: a) tet sin t dt

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Q: Which of the following is the general power formula for integrals whenever n # -1? Sx"dx = x"+1 + C…

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Q: Find the integrals below. а) / 5x dx b) S x2-3x + 2 dx X+1 dx c) S

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Q: 4. Calculate the following iterated integrals by hand. Show all steps. (a) (b) (c) -dr dy

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Q: Evaluate the following improper integrals provided they conver dx a) S Vx-x2

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Q: 1 d.r. x² In(x) Consider the inmproper integral r10

A: The solution is in step 2

Q: Calculate the following integrals: a) S(x-- - 2x?)dx

A: Consider the integral: ∫x-2x-2x2dx

Q: compute the given approximation to the integral.

A:

Q: A. Evaluate the following integrals. 1s (*2* -) x, 2х — 3' dx + 1. S x+2

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Q: Evaluate the improper integral :S e dx

A: See the attached file for a step by step explanation to evaluate the given improper integral.

Q: Define the following improper integrals integral -1 to 0  f(x) dx

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Q: Evaluate the integral. | (In(3.x))² dx = +C

A: From the given problem: I=∫ln3x2dx  ....(1) Let, t=3x So, ddxt=ddx3xdtdx=3dx=13dt Nw substitute…

Q: 1) Calculate the following integrals 1_dx a) S 4x²+25

A: Given; I=∫14x2+25dx    .....(1)   As we know that; ∫1x2+1dx=tan-1x+C

Q: Evaluate the following integrals: dx x In x 2.S da 1+x 1+x?

A: 1. ∫dxx ln x2. ∫1+x1+x2dx

Q: In y -dy 4

A:

Q: Calculate the following integrals. (०) / जरेगार dx dr (b) */4+(In r)?

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Q: Evaluate the following integrals ii. fx cot-'x dx .

A: Solution is given below:

Q: etermine the following integrals by using (IF) 1. S dx 4x2+4x+1

A: Topic:- integration

Q: 1) Calculate the following integrals. b) √₁6x²=1 -dx

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Q: d) Prove the results of the integrals 3 dx = 2+ In (2)– 4 [In (5)– In (3)]. x² +3x +2

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Q: Evaluate the integral. dy y4 – 16

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Q: 22 Calculate the value of the integral over the following C curves, a) C:|2+1| = 1

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

Q: Which of the following integrals represents the surafce area of the curve y = 3x +1 for 2 <x<5? S=…

A: Directly use the formula for the surface area of the curve and substitute the given equation of the…

Q: 11) What are the following integrals? a)S f(x)dx b) S xdx

A: Calculate the integral value: a) ∫abfxdx b) ∫xdx Here we use the integral formula: ∫xndx=xn+1n+1+c

Q: 4. Evaluate the following improper integrals or show that it diverges. (a) S T dr (c) S In z dr (b)…

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Q: 2. Evaluate the fellowing Integrals:- e dx dx ans (z a.

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Q: Evaluate the integral of ((x dx)/(x + 1)8) from o to 1.

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Q: Evaluate the integral In 23 In y s s ex+y dx dy.

A: Given: ∫1ln23∫0lnyex+ydxdy

Q: Which among the following is an improper integral? In3 ex xp- |4– ex In2 e 1 X/16 - Inx e 1 x Inx…

A: Improper integral :It is a definite integral . There are two types of improper integrals :- First…

Q: 3. Find following integrals using method of substitution: Sze z dz a. 2 x2 b. S /1+x

A: Consider the provided integral, ∫ze-z22dz Find the expression for this integral using substitution.…

Q: Evaluate the integrals. ∫y2/(y3 + 27)dy

A: Given: ∫y2y3+27dy

Q: Compute the following integrals: et? + + 4 2x ex? + 4x2 + x 1. - dx

A: Solution of this question is