3x2-3 and y(0) = 8, then y(1) = If dx 4. 12. 0. 8 6.

Q: 4x – 3 - 3 Given : | dx x² (x² + 9)

A: Given : ∫4x2-3x2x2+9dx

Q: 7. Find. V2x dx - 1

A:

Q: 3. Scse*x dx

A: The objective of the question is evaluate the indefinite integral.

Q: x2-4x dx 3) S (x+1)(x²+4)

A:

Q: f(x)dx = 2, 5 and 8 f(x)dx = -5, then, 8 f(x)dx = -3

A:

Q: Evaluate [(e²/² - x)(e²/² + x) dx. Show your work.

A:

Q: 2х+3 3. S ·dx (х+1)(x2+4)

A: We have to find the given integral. We will use partial fraction decomposition. We know that-…

Q: бх-7 7. S dx (2х+1)(4x2+1)

A:

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

Q: S2x3-4 x²-x-3 dx х2-2х-3

A: See the details solution in below

Q: 4-y2 dx

A:

Q: (iv) S х2 +3х-1 dx x3-1

A:

Q: 13. dx/(x²-4)

A: Since you have posted multiple problems we will answer first problem for you. If you need any other…

Q: S- 5e2*dx 9e 4x - 6e2+1

A:

Q: 5e2x dx e2x + 11e* + 24 + 11e* + 24

A:

Q: What values of a and b maximize the value of (x-x²) dx.

A: Find your answer below

Q: S x²-x +2 -X X³ + 4x -dx

A:

Q: 2x* - X* dx 「奈 3. スx* + 1

A:

Q: e4z+1 dx e2r – 1 17.

A:

Q: a) Evaluate x* - 4|dx and L (x* - 4 )ax. Do you get the same answer for both?

A: Answer

Q: 2x (x-a)² dx; a is constant

A:

Q: 10. fS'(x)dx -4

A:

Q: 2. S (2x-5)dx x2-5x+3

A:

Q: f3xcos(4-x*)-8xV4=x² dx s(4-x²)-8x/4-x² dx —:

A: Let us solve the integral using substitution method in the next steps.

Q: 2 S (x² – 4| – |æ – 1)) dæ - 4| – |x – 1|) dx -2

A: Definite integration

Q: x(x²-x+2) dx is equal to 3

A:

Q: 5. Show that (x² + 1)e-* dx = -x²e-x – 2xe-x – 3e-x +C

A:

Q: e3x dx ex – 1

A: Given: I=∫e3xex−1dx

Q: 1 The value of f|5x – 3|dx is

A: Integration of the absolute valued function

Q: dx S- x4 - 1

A:

Q: (iv) S: (1-x²)z dx x8

A: Given:

Q: 2. 5x - 2 (x + 3)² S dx.

A:

Q: X -2 5. S dx х2 (х — 1)

A:

Q: Find the following indefinite integrals:

A: Now,

Q: 4x2-5х+6, 3. S(*-*+*)d *“)dx x2

A: We have two types of integrals in general, namely definite and indefinite integrals . The definite…

Q: 5- (2xe" + e')dx + (x² + 1)e³dy = 0

A: solving given DE by separation of variables.

Q: ii) ∫7x-25/(x-3)(x-4) dx

A: Given,          ∫7x-25x-3x-4dx

Q: x-3 dx V16-x² (16-х2

A: Given,          ∫x-316-x2dx

Q: 11x3cos(x2)dx

A:

Q: 6. S (2x+3) dx (x2+3x-6)9

A:

Q: .6 6 If | F(x)dx=12, what is the value of | f(6– x)dx?

A: Using property of definite integration.

Q: [4] s **-2x³-2x x²+1 [4] S² > [5] S dx dx ex-1

A:

Q: 9. S." §, x*V9-x dx 16 dx Vx-2 10.

A: We need to evaluate the given definite integrals, to sove we will use the substitution method.

Q: (3) S 4-x² dx

A:

Q: 5 S Ix² x- 6|dx -5

A: The given integral,            ∫-55x2-x-6dx

Q: a. S(x² – 1)e*²-3x dx

A:

Q: 2 dx X + X - e メ-

A:

Q: e6x (a) : dx 4+ e6x (b) /: dx 4+ e6x 3 (с) dx V4– x2

A: Since you have posted multiple questions i can answer first three as per our company guidelines…

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

A: Sol