Evaluate x²|1 – 2x| dx.

Q: (21 + V3)/3 11 dx Evaluate 50 + x - 14x

A: Explanation of the answer is as follows

Q: [(2x -1)3– x )dx = + 8. 0 3.

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Q: 9. Evaluate -2x +9x-1 dx (x² – 2x +1)(x +2) -

A: Solve the problem using partial fractions

Q: dx. Evaluate J 2x²+3x+1

A: We have to evaluate the ,  I=∫12x2+3x+1dx

Q: dx i let x-= 4X-X2

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Q: 26x°- 52x+3 dx. Evaluate x2 - 2x

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Q: D Evaluate 2x dx (I+ x)3

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Q: Q3. Evaluate f: 2*+1-5x-1 dx 10

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Q: 5 dx. 2. Evaluate J-∞x²+25

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

Q: 3 Vx dx 2 x+1 Evaluate

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Q: Evaluate fcos-¹(x) dx

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Q: Find the indefinite

A: Consider the integral

Q: (w - 3x +3)dw + ( 3w + x + 9)dx=0

A:

Q: x3 dx J4- x4

A: ∫x3dx4-9x4Multiply & divide by -36 =-136∫-36x3dx4-9x4since, ∫f'(x)f(x)dx= 2f(x)

Q: Evaluate dx 2 1-x

A: We have to evaluate ∫23x1-xdx. We know that ∫dxx2-a2 = 12aln x-ax+a+C

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A: Given: verify that ∫26x3dx=320 for verifying given integral we solve left hand side

Q: 3 csc2 V1-4cot² x x dx

A:

Q: x-1 2 x² + x -dx

A: As per the question we are given an indefinite integral of (x-1)/(x2 + x) which we have to evaluate.

Q: 1/2 dx 2 -1/21-x

A: We will solve the problem

Q: 2. (a) Evaluate [ x* V1+4x² dx. (b) Evaluate 8x° +13x dx. (x² +2)²

A: (a) We have to evaluate the following integral: ∫01x21+4x2dx Then we get,…

Q: 2nsin (пx?) dxdy x2 0,

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Q: 3x + 2 Evaluate dx. (x + 1)(x + 2)

A: The expression 3x+2(x+1)(x+2) cam be split into simpler fractions using partial fraction.…

Q: 2x + 1 Evaluate dx x2 - 7x + 12

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Q: 21-y 2. Evaluate [(x + y)dxdy. 1 0

A: 2. We need to evaluate the following iterated integral  ∫12∫01-yx+ydxdy

Q: Evaluate the function: 1 dx x²/3 () 1+a!/3

A: Given: ∫1x231+x13dx

Q: Show that (xcos(2x)dx=. A-2 8

A: LetI=∫0π4xcos2xdxPut 2x=udifferentiate on both side2dx=dudx=du2As x→0 then u→0As x→π4 then…

Q: Evaluate. (4x + 5x²) dx -2x dx 8. 9. dx 10. -5 for x 2

A: To evaluate: ∫-12(4x+5x2)dx Solution: We know, ∫xn=xn+1n+1+C    ..(1) Here, ∫-12(4x+5x2)dx On…

Q: x+ 18 (d) J3 dx x2+x-6

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Q: 2. Evaluate -2* dx xe

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Q: Evaluate 2х— 7 -dx J x2 — бх + 10

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Q: x(3-5х) J - (3x-1)(х-1)* # 2) Evaluate: -dx-

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Q: dx Evaluate Vx+2x+x3/2

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Q: 5x 2 Evaluate: f fx fdz dy dx 2

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Q: a) Evaluate -5 S₁v 1 √√4 − (x − 3)² dx -

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Q: 2x?+9х-1 1. S x(x2-1) dx

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Q: x² dx. Evaluate: /2x3 -1 -1

A: We have to evaluate the integral

Q: +j =6- d 5x+(/x + %3D dx x² 2.

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Q: -9 (x-1) 8. √x dx

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Q: 2. (a) Evaluate [ x*V1+4x° dx.

A: We are given : ∫01x21+4x2 dxLet I=∫01x21+4x2 dx Let x=12tan t⇒dx=sec2t2dtNow, when x=0 , t=0when…

Q: x +2x dx. 4 13. Evaluate J- (** +3x2 +9)

A: Integration by substitutions

Q: dx = - 4 In|x| +C %3D

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: r2 Evaluate xe* dx. хе

A: Find the value of definite integral.

Q: Evaluate ∫x3 √(1 - x2) dx using a u-substitution

A: It is given that,∫x31-x2dx     We have to evaluate using a u-substitution.

Q: -3 +х-5x"+3x' +3х dx Evaluate x' +x- 2

A: Given: ∫24-3+x-5x2+3x3+3x4x2+x-2dx

Q: iii) So z dx 1+x2

A: Given: ∫01 x1 +x23dx To Evaluate given integral Proof: We will evaluate the given integral by…

Q: SV2*- 16 dx 2.x

A: Consider the integral: ∫e2x−16dxApply u…

Q: x3-1 dx J2+2x+5

A:

Q: -2 х 6. dx 1-x

A: Topic = Integration use ∫1xdx=lnx+Clnx⇒x is NOT defined for negative values of the independent…

Q: Show that dx (a) - x² +1 2

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

Q: X 2 dx = V4-x2

A: I=∫01x24-x2dx =∫01(4-x2)+44-x2dx =∫014-x24-x2dx+∫0144-x2dx =∫014-x2dx+4∫0114-x2dx Here  ⇒∫a2-x2…