2dt t/4t4 – 1

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A: Consider the given integral:

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Q: Evaluate the integral.

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Q: dz 2 t´ + Zz-3

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Q: d.x (a) Evaluate the integral In(8x) using the substitution u = ln(8x). d.x +C T In(82)

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Q: Which of the following integrals is equal to (3x-5) dr if u=3x-7? (A (u+2) du 8/3 -2 -1 / (u-2) du…

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Q: Evaluate the integral. 4π S t² sin(2t) dt

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Q: Compute the given integral. +C

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Q: Evaluate the integral of (t2) / √(1+t2 )with respect to t.

A: It is given that, f(t)=t21+t2 It is known that, ∫1(x2+a2)dx=logx+x2+a2+c and…

Q: Evaluate the integral. +1 dt Vi 0.

A:

Q: Use the method of u-substitution to evaluate the given integrals. 4t dt 2 – 812

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Q: Evaluate the integral from 0 to pi: ∫cos4(2t)dt

A: ∫0πcos42t dt

Q: Evaluate the integral. ∫0 π Cos42t   dt

A: Given: I=∫0πcos42tdt we know that 1+cos2θ=2cos2θ similarly, cos22t=1+cos4t2 now substituting value…

Q: Evaluate the integral. et i + 3t2 j + In(5t) k) dt + C

A: We have to evaluate the given integrate…

Q: evaluate the integral; ∫ [5,1] t/1+t^2 dt

A: We have to find the value of given definite integral. To find that we use integration by…

Q: Evaluate the integrals

A: Solution -  Given Integral equation - y = ∫π201+cos2t2dty =12∫π20dt + 12∫π20cos2t dtUsing…

Q: 1. Determine the following integrals: 1- 2 (a) dar- (b) |

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Q: Evaluate the given integrals. 5. J(1 – cos 0) csc²0 d0

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Q: show the steps of this integral: | dxp In p = In a H

A: Given that H=-∫0adxρlnρ This can be written as, H=∫0a1ρdρ

Q: 1. Evaluate each of the following iterated integrals. 4-y2 2-y C.

A: Given: I=∫02∫04-y2∫02-yzdxdzdy We know that; The Power rule: ∫xndx=xn+1n+1+C ; n≠-1

Q: Sy² sin(3y³ + 4) dy

A:

Q: (t+ 3)² dt

A: We have to find the integral: ∫t+32t4dt Simplifying using identity a+b2=a2+2ab+b2,…

Q: 4t dt 2 - 812

A: To find the given integral integration (3 to 5) 4t/(2-8t²) dt

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Q: Evaluate the improper integral t* e-2t 3+e-4t at

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Q: Evaluate the integral: J22 SVA-2 01- [] π [] +C dydz 4-2² e² +²

A: double integration using polar form

Q: Evaluate the integrals ∫(t + 1)2 - 1/t4 dt

A: To evaluate the integral: ∫t+12-1t4dt Evaluating the given integral.…

Q: Compute the given integral. - 522 xe -522 10 X+C

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Q: Evaluate the integral. |a cos (6 x) de = | + C

A: topic - indefinite integral

Q: 1. Evaluate each of the following iterated integrals. a. " e**ydxdy

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Q: Compute the given integral. dx +C

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Q: Evaluate the iterated integral. In 3 In 4 e 4x +y dy dx 0. 1.

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Q: 1 I. 1+ Vx xp:

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Q: 1/4 cos² (4t – -) dt

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Q: 81. The particular integral of x2 d²y A) 3x +y = is |3D de 6x 769

A: We can find the first and second derivative for the given options and check in the  differential…

Q: Evaluate the integral . Identify the u and the du. (5x2  +  1 )2  (10x) dx

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Q: find the integral from 1 to 4 of (3t^(3/2) i+(t+4)(√t)k)dt

A: The given expression is ∫143t32i+t+4tkdt. Evaluate the value of integral. Here we use the formula…

Q: Find the integral. 21) + e3t) dt

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Q: 1. Evaluate the integral using the given substitution xcos(9x2)dx u = 9x2

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Q: Evaluate the integrals in ∫2 t e-t2 dt

A: Given:2∫ t e-2t dt