(1) f (1) x²(x³ +1)5 (x³ − 1)5 dx -

Q: (12) Find the Value of b such that: [3x² dx = 27 (A) 6 (C) 9 (B) 3 (D) none of these 4

A: Step 1:To find the value of b such that ∫0b​3x2dx=27, we need to solve the definite integral: Step…

Q: Given that (a) (b) Prx [ FLX f(x) dx = 3 and f(x) dx 2 [²(x [²Px) dx - [Px) dx f(x) f(x) f(x) dx =…

A:

Q: (в—7)

A: The integral given is ∫x-7x-13dx. Simplify the integral ∫x-7x-13dx using substitution, Substitute…

Q: (a) / (2.x4 + Vx3 + 4e* + + 8) dx - (b) / = x3 + 3x – 4 dx - x2 (c) (x + 4)(x³ – 9) dx .3 -

A:

Q: (e + x + 2)dx 3.

A: The sum rule for integration states that ∫fx+gxdx=∫fxdx+∫gxdx. The integration formula for…

Q: Find 4 [3f (x) – g(x)]dx = i if 4 4 |r)dx = 4 and g(x)dx = 20

A: This question is related to definite integration, we will solve it using given information.

Q: (d) dx (e) S,(4x + 2)5 + (6 – 4x) dx (f) S,' 4x3 – 3x* dx

A:

Q: (d) d.x (x-3)2/3 1.

A: The given question is from the topic of Integrals

Q: Find f(x)dxif 5 | f(x)dx = -8 and / f(x)dx = 3 6. | f(x)dx = i

A: Solve the following

Q: –1/2 | (x (x² + x) + 4)dx.

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

Q: Is the answer correct?

A:

Q: sec(r) dx \ x2 – 3x +4 d

A:

Q: (c) [ √4x² X -dx

A: The given integration is

Q: -1 4 A = 1 -2 -5 3 7

A: 2-14 1-2-5 037

Q: Find [2f(x) – g(x)]dx = i if f(x)dx = 4 and g(x)dx = 50

A:

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

A:

Q: ((x + 1)5 + 3y)dx − (x + 1)dy = 0

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: - Find (a) for dr (b) fxºdx (c) [10e-de 10eª0dx

A: we can answer only three subparts, or the first question and the rest can be reposted. No more than…

Q: A) a B) b ²¹dx = √( + g(x)) dx, then A + √² g(x) dx is equal to x³+x A. -1 B. −1+In(5/2) C. 1 D. -1…

A: Given; ∫x2-1x3+xdx=∫Ax+gxdx   As we know that; ∫1ax+bdx=1alnax+b+C

Q: 1 S (x– 2)(4x² + 1) dx х — 2 4x¯ +1

A:

Q: dx x (1+a2)

A: As per our guidelines only one question can be solved. Please find the solution for 1st question…

Q: S Vx + 3(x + 1)dx

A:

Q: ха-1 dx 1+x4 (2) 8.

A: The given integral is: ∫0∞xa-11+x4dx

Q: (iv) S: (1-x²)z dx x8

A: Given:

Q: Q Solve the non linear differential eguation )= ex

A: To Determine: solve the nonlinear differential equation. Given: we have an equation eydydx+1=ex…

Q: 1 (x2+2x+ 1) dx -1 16 3 16 0 8 3

A: Given:The integral is

Q: Find [9f(x) – g(x)]dx = i if f(x)dx = 2 and g(x)dx = 30

A:

Q: Find the angle 8 in the figure. (Assume r = 5 and s = 10.) radians

A: Given, r=5 and s=10