.2 3. If o (x) = f Ví dt, then 0 (a) 2x2 (c) O do dx (6) SA (d) 1. is

Q: x=5, evaluate: a. 12 b. Jasnde d. f19f(x)-12g(x)|dx

A:

Q: 6 .6 If f(x)dx=10 and f(x)dx=3, then | f(4 – x)dx=? A В 3 (c) 7 10

A: Given that a integration problem and we solve this problem by using general formulas of integration.…

Q: dy If 2y = xlnx, then dx (In x)xinx (xinx) In x (b) (d)(In x)xanx) 2

A:

Q: Step 4 Finally, determine(-3x + 7) and (x + 7) and simplify the result. dx dx 1. du 1 dv + U dx V dx…

A: formulas we use: ddxf+g=dfdx+dgdxddxkx=k; k is a constant.dkdx=0; k is constant.ddx(x)=1.

Q: 1 2x Evaluate [(4x-7)ay dx.

A: To evaluate: ∫01 ∫x22x (4x−7)dydx Let I=∫01 ∫x22x (4x−7)dydx First evaluate with respect to y taking…

Q: 이 x 2 + .dx 2. Jordr V1-p3

A: I have explained everything with in the solution .please go through that.

Q: x²V4x +1 dy then dx If y = In (x³ + 5)3

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Q: Determine C when x=y=0 (xy + x)dæ = (x²y + æ² + y³ + 1)dy

A: Given that xy+xdx=x2y2+y2+x2+1dySolution…

Q: of Find (1.-7) if f(x.y) = 2x2 + 4xy - 5y? + 4x - 9y - 9. dx of (1, -7)-O (Simplify your answer.)

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Q: 7 49 – x² dx 2. Compute the value of

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Q: | f(x)dx = 3 and f(x)dx = 7 , then (2f(x) +3)dx = If 4

A: TO FIND ∫43(2f(x) +3) dx GIVEN - ∫03f(x) dx = 3 ∫04f(x) dx =7 USE THIS PROPERTY TO SIMPLIFY- ∫abf(x)…

Q: Below are attempts at u-substitution by students. Explain where each student went wrong, then…

A: Given,.

Q: If fe F dr = Sc(x - 2y³) dx + (x²y) dy, what is F?

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Q: 15 .3 Suppose f(x) da = 2. f(x) da | f(x) da = 5. What is | f(æ) da? 3, and -8 -10 10

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Q: 1. = fVx*- Jーxa 4 %3D - 2. (x? +1)²(x+ 2)dx 2х-4 dx 3. V x-4x+1

A: 1. ∫x2-x4dx

Q: |(6x – 1) dx

A: Given Data: Integrand: ∫146x-1dx The power rule of integration is, ∫xndx=xn+1n+1+C

Q: Evaluate f(f(x+2y)dy) dx.

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Q: dx 8. J x*V5x-x

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Q: Differentiate the following function. 6x2 +5 y = x2 +1 dx (x² + 1)< dy (x² + 1) • : (6x² + 5) + (6x²…

A: You just need to apply quotient formula in order to solve this.

Q: S (In 2x2 dx

A: Evaluate the integral :    ∫ln 2x2 dx

Q: 6. If f(x)dx = 5, f f)dx =2, and , f(x) dx = –1, find i f)dx. а. —2 b. 2 C. -3 d. 3

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Q: 3 d²y If the functions are x = e-t and y = t+t + 1. Determine its dx2

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Q: Evaluate e dx 3 2 + C O x + C O 2/x + C In e + C

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Q: 3. fz √z dz 4. (2x² 3x + 5) dx -

A: 3. ∫zzdz4. ∫2x2-3x+5dx

Q: 5.[15] Evaluate V1+7x dx a. Identify u= b. Find du=

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Q: dy Find the dx of the function y = 25" 34x² O a. y = 2°a 34* (2ln5 + 8x²ln3) O b. y = 2°r 3t (In2 +…

A: Given; y=25x34x2 As we know that; The Product rule; f·g'=f'·g+f·g' The Chain rule; fgx'=f'gx·g'x The…

Q: 12. | (1피+ 1r-2) dr

A: To find the integral  ∫-14x+x-2dx Apply the sum or difference rule, ∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx…

Q: b) Evaluate f v1 – x² dx.

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Q: 3.ƒ _(x−1)² dx √x

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Q: 11. Evaluate 9-y² LS [[V²=2³² (x² + y²) ² dx dy -3 0

A: We need to evaluate the double integral given by :

Q: Find p, q if f,º f(x) dx – L f(x)dx = [" 5(x) dx. (Give your answers as whole or exact numbers.) p =

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Q: - 3-z2-y 2. Evaluate L* L z dz dy dx -5+x²+y²

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Q: dx = 2, evaluate If (f(x) dx = 5 and -1 f(x)| dx + f(x) dx. (Jan 18) х +

A: Integrating a function within specific limits of the variable is called definite integration. The…

Q: -3 If L f(x) dx = 5 and f(x) dx = 6 then i f(x) dx = O 10 O 9 O 1 None

A:

Q: -7/2 + X ") dx (b) x + dx . Evaluate (a) | (3° + e*

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Q: Find the value of (x)) dx if f(x) dx=11 and f(x) dx=3.

A: here we have to find the integral vaule