y = (x – 1) 2x – x² + arcsin(x – 1) %3D - - - O - 12x – x² O - 2/2x – x² O V2x – x2 O 2v2x – x²

Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)2 + dx y * logy x *

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Q: Evaluate the integral. V3/2 5x2 dx V1 - x2

A: Consider the trigonometric identities 1)  cos2x = cos2x - sin2x = 1- 2sin2x 2)  cos2x + sin2x = 1 3)…

Q: find integral x3 3) S dx /1-x²

A: We have to find the indefinite integral

Q: Reducible to Homogenous method dy X-y-3 x-y-1 dx

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Q: Evaluate the integral. V3/2 19x2 dx V1 - x2

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Q: find the absolute extrema of thefunction on the closed interval. y=x^{2}-8 \ln x,[1,5]

A: Given:- function y=x2-8 Inxdefined on the interval 1, 5 The derivative of the function is y'=2x-8x…

Q: x² + x - 1 dx J, x(x2 – 1) is convergent or divergent.

A: We have to solve the integral and check it is convergent or not

Q: 1: Evaluate the integral 3x - 1 (x + 4)(2x - 1) I -dx.

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Q: Evaluate the integral.   ∫0 1 (x2 +1) e-x dx

A: Evaluate the integral.   ∫0 1 (x2 +1) e-x dx

Q: 1. Evaluate the integral 5x + 1 dx 2x2 - x -1

A: We can evaluate the given integral by using the partial fraction method.

Q: Ssint2x)dx = 2cos(2x) (2x) + С -cos(2x) + C O 2 cos(2x) -cos(2x)+ C

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Q: -0.8 If y = S° 0.2 + 25x – 200x² + 675x³ – 900x* + 400x5. | Find the integration analytically.

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

Q: Find a ≤ b such that

A: ∫abx2-9dxApply the Sum Rule:…

Q: b) Suppose x # 2. Find dif dx In y = In (x - 2)² √x² +1

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Q: 4x2 Calculate the integral: dx 3/2

A: I use trigonometric substitution to calculate this integral to see full solution please visit 2nd…

Q: 18x? Evaluate the integral: -dx V49 – x2 -

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Q: 5. Find the integral 1 -dx x -5x +6

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Q: -1 2x Evaluate the integral dx = 0 x*+1

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Q: Use integration by parts to prove the reduction formula: п-1 S (In x)"dx = x(ln x)" – n [ (Inx)"-! п

A: 2

Q: (a) Evalate the integral||xydy dx. 12

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Q: π/2 g(x) = 2x + 4 sin² x g(t) dt. - n 0

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Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)² dx y logy x * * -

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Q: a) [ Evaluate the integral 4x - 1 (x + 2)(2x - 1) S -dx.

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Q: 6 If the substitution y = xº is made, the 64 3√√y 3 + √√y integral [ 1 dy will become

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Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)² dx y * logy x |

A:

Q: dx 2 (1+3x)2

A: We will find the integral as following.

Q: 1. Use the delta method, 2 BONUS MARKS y = 5x² dy dx = lim h-0 f(x+h)-f(x) h to find dx for the…

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Q: Find the general form of the antiderivative of g(x) = - cos4x

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Q: Evaluate the integral. 3x-7 (a) S- dx x2-2x-8

A: Answer and explanation is given below..

Q: O f(3x² + sec² 2x) dx

A: Given query is to find integral.

Q: 2. Evaluate the integral: 2xe-**dx -0

A: topic - integration

Q: 1. S =dx = -Arcsin x√x²-4x-1 +2 X √5 +c

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Q: 3. Find the integral x² +12x +12 dx x' - 4x

A: Given,            ∫x2+12x+12x3-4xdx

Q: 4- 13 + 6y = 0 dx

A: We have to be find

Q: 3. Find the integral. 2x dx x2 + 10x + 29 а.

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Q: (a) Evaluate the integral [x (x* -1) ´dx by using substitution.

A: To evaluate the given integral ∫x3x4-12 dx by using substitution.

Q: The equation (y-x)=x(dy/dx) is Bernouli (y^n> 1) O linear in x O Homogenous O variable separable

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Q: Find the integral +C 1 dx x² – 16

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Q: se N.P.M. to estimate the root of -X = e -X for an initial of Xo =0

A: Here f(x)=e-x-x,  x0=0. We estimate the root of f(x)=0 by using N.R.M.

Q: Q4: To evaluate the integral fcos' xdx using the reduction formula of cosinc function

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Q: #@3 g (x; y) = 7x3 - 49IXY + 7y3 Find and elassify all the extreema of the fine tion

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Q: Let y'=sinxy and y(0)=2 Approximate y(4) using Euler's method with step sizes of .25

A: The solution of a differential equation is defined as the function that satisfies the differential…

Q: What value of x > -1 maximizes the integral / t²(3 – t)dt?

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Q: Evaluate the Double Integral. 4 V16-x2 b. 2x dy dx

A: We have to evaluate

Q: 4 VI 2. Evaluate the integral: xy dydx. 2

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Q: 3 Find absolute extrema for fCx) = x°-9x´+15x -3 %3D in terval [o,3] Oへ

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Q: 4) Evalvate the integral E 4 1+x² dx

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Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)? dx y logy x

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Q: Find the general solution using Reduction of Order: x2y''-xy'+y=0 y1=ln x

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Q: the integral (dx)/(xsqrt4x2+1)

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