3. d dx Pick one by (and only one!) and prove it: [kf(x)]= = k f(x) d d.x d - [csc(x)]=-csc(x) cot(x) dx

Q: Evaluate 6x² (x³ – 1) dx

A: Given,          ∫036x2x3-1dx

Q: 8 If f.°³ F(x ³ f.° 9(x. f(x) dx = 39 and 8 d fº[31 g(x) dx = 16, find [3f(x) + 5g(x)] dx.

A: NOTE: Refresh your page if you can't see any equations. . here we have ∫08fxdx=39 ∫08gxdx=16

Q: d Find (5 In(x)) dx

A: Given query is to find the derivative of the expression.

Q: Find f(x) dx = -3.5 -3.5 and 2f(x) – 3 dx = -1

A: Given: ∫-61.5fx=2∫-6-3.5fx=3∫-11.5fx=4

Q: tan-lx dx 3+ 3x2 1. Evaluate

A:

Q: 16. / cot(z) dr 17. cot (x) dr 18. csc(r) dr

A: (16) ∫cot(x)dx ∫cot(x)dx=∫cosxsinxdxPut t=sinx      dt=cosxdx we get-∫cot(x)dx=∫1tdt…

Q: Find [(x- sin(2x)) dx

A:

Q: 1. Find the first derivativ

A: Given that,

Q: 3. Evaluate f x sin2 (x²) dx.

A: Given I=∫x sin2x2 dx To Find I

Q: IF f(x) = 13sin(x)-8e*. Calculate: df(x) dx =

A:

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) ​

Q: Let f³ f(x)dx = 12, f³² ƒ(x)dx = 3, få ƒ(x)dx = 4 ƒ² (2ƒ(x) — 1)dx Find

A:

Q: 2 + Vx dx. (a) Evaluate 1 dx. x + x(ln x)2 (b) Evaluate

A: Explained below

Q: Assume the following: f(x) dx ce. ƒ(2) dx = 2, ª f(z) dx = 3, 9(z) dz = -1, and + [°²9(2) ² = 2, […

A: