1 (x2+2x+ 1) dx -1 16 3 16 0 8 3

Q: 3. Evaluate the integral. dx B. + 1 А. 8 2 С. 4 c.- D. - 2 6

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A: Given: ∫x ln2 (x) dxFormula: (ln (x))'=1x∫ x dx=x22+C

Q: 2 Find 2(x² + 3x - 1) xp- b. (x+ IX2x - 1)ar – 1)' dx x(x + 1) + 2 – 2x – x² a

A: We Use partial Fraction to separate the denominator and then integrate with respect to x.

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

Q: С 20 3x-1 хр. -X (3+3 (2) j² dx a Лх lo XS хр sự X Сў-12.d:

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Q: Evaluate the definite integral using the given values

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A: Topic:- application of integration

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Q: 3. (10 – 6y +e 3) dx -3x 2dy = 0 -

A: According to our guideline, we can solve only first question of multiple question. If you want…

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A: Disclaimer: Since you have asked multiple questions, we will solve the first three questions for…

Q: Y1 = x² + 2x + 1 Y2 = 2x + 26 dx y2 35 30- 25 20- y 15 10

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Q: S (2x² + 1) dx x3 - 3x +2

A: ∫2x2+1x3-3x+2dx This can be written as  ∫2(x2-1)x3-3x+2+3x3-3x+2dx=2∫(x2-1)x3-3x+2dx+3∫1x3-3x+2dx

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A: Evaluate the given integrals

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A: First simplify the integrand to get the simpler integrand.

Q: 3. dy = (x - 3y)dx ans. 9y = 3x - 1 + ce 3

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Q: 5. (3x-17) dx / (x² - 6x + 10) 11

A: As per our guide lines we are supposed to answer only one question. Kindly repost other questions as…

Q: -3/2 1/2V2 dx 2 dx 5. 6. V9 - x VI - 4x

A: Integration of the functions and substitution of the limits helps to find the solution of the…

Q: 8. (c) x³e 73e-2x dx 0.

A: To evaluate the below integral. ∫0∞ x3e−2xdx

Q: 2xy - 10y -x + 5 y - 6 xy + 5y + 2x + 10 -dx +- 0 %3D 2.x + 3

A: Separable Differential Equations: A separable differential equation is an equation that can be…

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Q: 8. (x² + 2xy 4y²) dx - (x² - 8xy - 4y²) dy = 0. ANS. x² + 4y² = c(x +

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Q: x² = 2y²(y-1) y² = 2x²(x+1) x² = 2y²(y+1) y² = 2x²(x-1) dx (3x²-2-²) 4

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Q: 3(x5 + x³) ez"+xª + 3(x6 +xª) +2 dx -2

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Q: 3/2 (-2x + 4) dx J1/2 | 16.

A: Note: We are authorized to answer one question at a time, since you have not mentioned which…

Q: 1. (xy² - x²) dx + (3x²y² + x²y - 2x³ + y²)dy = 0

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Q: 1 b. 4*(x³)dx -1

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Q: Evaluate the definite integral using the given values

A: Given: ∫26x3dx=320, ∫26x dx=16, ∫26dx=4 We have to evaluate ∫266x-18x3dx Solution:…

Q: √ 1 x²√2x-x² dx = x+¹√ √√2x-x² + c 3x²

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Q: x dx 5. J 3-x2-6x

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Q: 2. x°ー×- 8x ー1 dx x²-3X -4 2

A: according to our guidelines we can answer only three subparts, or question and rest can be reposted.…

Q: • 4 13х + 12 -dx x2 + 3x 3

A: ∫3413x+12x2+3x-4dxApplying completion of squares:=∫3413x+12x+322-254dxSubs u =…

Q: 23-4x-8 Integrate: 2E+4) dx 1)(r²+4)

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

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Q: dx 16. S 9x2-4 |3x+2 A. In +c B. In D. tn +C + C + C |3x+2 |3x+2| 3x-2

A: This is basic integration problem

Q: 2) (Зx2у + 4eУ)dx + (x3 + 4хеУ + 2у)dy

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Q: 2 S. x*- 4x +4 dx (メ-2)(x4) |

A: Solution: Consider the given integral is: I = ∫x2-4x+4(x-2)(x2+4)dxI = ∫x-22(x-2)(x2+4)dxI =…

Q: ii) ∫7x-25/(x-3)(x-4) dx

A: Given,          ∫7x-25x-3x-4dx

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A:

Q: (4(x2-1) dx x²(x+2)

A: We will use partial fraction here

Q: a) | f(x)dx = -10 %3D 4 b) f(x) dx = -10.5 4 c) f(x) dx = -17.5 10 d) / f(x) dx = 9 %3D 10 e) -5…

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Q: (3x² – 6.xy)dx +(-3x' – 2y)dy = 0

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Q: 5. j(4x²-5x+4)*(8x-5)dx 6X dx x ²-5

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Q: 4x+5 x2+x-2 5) 6) 2=1 +1 7) fx.tan-1x.dx dx =

A: To evaluate the given integral.

Q: 10. f (Se e-3x XE -3e*-4e*)dx 4e)dx e-2

A: Solution: The expression can be written as

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Q: (х2-2х+11)dx (x2+3х-4) .2.

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Q: rlog 2 Vex – 1 dx -2 S, x8Vx2 – 1 dx x² x8 dx (a? Loc2)7

A: Sol