Suppose that [ f(a)da = 7, and b) ²9(2 g(x) dx = 29, compute the following integrals: 5 S* 158 (2) - [5f(x) - 4g(x)]dx = f(x) dx = -7, and 5 [*[3ƒ(z) + 2g(a)]dx = g(x) dx = 13, and

Q: Evaluate 6x² (x³ – 1) dx

A: Given,          ∫036x2x3-1dx

Q: Scosh(2tn(x)dx

A:

Q: f(3x + 2)² dx

A:

Q: 14 6,¹ 3 Suppose f(x) dx 3 S f(x) dx = [ 14 = 15. Find

A:

Q: (x² (а3 — 2)da 4x +

A:

Q: Evaluate (3x + cos 4x) dx

A:

Q: If SeF dr = [c(-5x + 3y² ) dx + (x³y) dy, what is F? %3D F =

A:

Q: –1/2 | (x (x² + x) + 4)dx.

A: Given,            ∫04x-1/2x2 + x + 4 dx

Q: Evaluate x x-8 dx.

A: To evaluate the given integral.

Q: Jx (x* +1)* d

A:

Q: (3) S x²Vx + 1 dx

A:

Q: flx)=x =X-5 (x)= Find .f)

A: Here, the given function is: f(x)=x-5, g(x)=x2

Q: 3x2[x18 + x15 sinh(ax³)] dx

A: Given that ∫3x2x18+x15sinh(ax3)dx, 3∫3x2x15sinh(ax3)+x18dx Take u=x3→dudx=3x2,…

Q: If f(x) = 18x2 + 96 3 ³√√x' find f'(8).

A: Given Function:- fx=18x23+96x3

Q: Evaluate d/dx { In√(x+1)}

A:

Q: [2] (a) fe In (x²) dx (b)²x² In(x) dx

A:

Q: Find f′(x), if f(x)=(x4+1)(3x−1).

A:

Q: x +1 dx x(x² + 4)' (f) | #(2² + 4) ع و ش

A:

Q: Find | [3f(x) – g(x)]dx : i if 6 f(x)dx 2 and g(x)dx = 30 %3D %3D

A: Given: I=∫163fx-gxdx And ∫16fxdx=2 ; ∫16gxdx=30 We know that; the sum rule: ∫fx±gxdx=∫fxdxdx±∫gxdx…

Q: -1)/(x4))1/2

A:

Q: x(x2 + 1)3 dx J-1

A: Consider the integrals, ∫-11xx2+13dx…

Q: -x dx = 2n

A: Given  To prove

Q: 4. (a) Find dx (b) Using the result from part (a), evaluate. x So (1 + 22)3/2 (1+22)3/2 dx.

A: ANSWER : (a) ​  ANSWER : (b) ​