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

Q: x1 J: (x2+2x)2 dx= (x2+2x)3 C (x2 2x)3 C + 3 (x2+2x)3 +C 6 22-1C + -2 2x)1+C

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Q: Find A and B such that 2x-1/(x+1)(3x+2) = A/x+1 + B/3x+2

A:

Q: 1x?x+y SS (x +2y + 4z )dzdydx 0 x x-y

A: Explanation of the solution is given below...

Q: Find the antiderivative of  x4(5x5 + 1)5

A: To find out the antiderivative we use u- substitution method

Q: If f(x) ' (1 ) cos (x)

A: We have f(x)=xcosx. So,            f'(x)=xcosx'            =xsecx'            =x'secx+secx' x…

Q: (b): Evaluate: SS (16t³ – 12t² + 5)dt

A:

Q: PROB.NO. 4 VERIFY THAT (X - 3 )(X - 21) = (X - 21 )(X - 3) = Xx - 5X + 61 FOR [i 2 0] X =0 30 0 0 4

A: To verify the given expression is followed by matrix X .

Q: 2x+2 y = 5

A: Given : 2x+2y = 5x+y = 3

Q: Determine Dx[x(x-2)²]

A:

Q: Lt² V4-t² dt V(4-x)/(2\x) x(4-x)

A:

Q: Cakulate (3i+2j+k) • (i + zj - k

A:

Q: 2 X 2 X 0+ - 4 +4 dx =

A: C+C

Q: Does S = {x² + 1,x² – 1, 2x – 1} span P2?

A: we know dimension of P2 is 3 so any set which span P2 must have at least 3 elements. here given set…

Q: a) [(5x4 + 3x² + 2x + 4)dx b) [(Vx² + 7x)dx

A:

Q: (1 1x +15x* – 17x³ – 6x² + 7x – 4)dx -3

A:

Q: .2 2 S²6²³ (2x + 3y) dxdy 0 Find

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Q: = (2xy + z² )i + (x² +z)j + (y + 2xz)k, determine a possible value for .

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Q: Show that |Aut(Z2 × Z2)| = 6

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Q: 1 da (2a + 1) +1) 1. 8.

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Q: Evaluate V1-x-dx A. --(x+xvI– x-) +C B. (x+xV1%3=x) +C c. (x+xv1+x-) +C D. -(x-xVT-x-) + C xv1-x)+ C

A: Find your answer below

Q: Evaluate the following x4 + 4x³ + 7x² + 17x – 9 -dx | 1. x3 + 2x2 – 3.x

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

Q: Find xy² Una -dA, R= [0,4] × [-2, 2] x² + 1

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Q: b) 2(x4+1)5 dx

A:

Q: differentiate [x2+2][2x+3][1-4x] w.r.t x

A: We know that ddxxn=nxn-1 and ddxlnx=1x. We need to differentiate the expression: x2+22x+31-4x with…

Q: Find the J(2x + 1)³ dx

A: