2. One of (a)-(c) is incorrect. Find and correct the mistake. (a) - sin(y³) = 2y cos(y?) (b) dx sin(x²) = 2x cos(x?) dy (c) sin(y?) = 2y cos(,?) dx

Q: 6. S sin x In(1 + sin x) dx

A:

Q: 4. S sinºx dx

A: This question can be solved by applying the concepts of integration of trigonometric functions.

Q: (sinx)" dx is:- 4) The solution of (sin x) dx A) (sinx)' dx B) C) Zero

A: ∫0πsinx7dx=∫0πsin7xdxWe know…

Q: 2. f cos³ (20x)dx

A: Given :

Q: sin(x)ecos dx COS X 8.

A: Given,

Q: 6. S 2sin´x sin(2x) dx

A:

Q: -. Solve for dy/dx a. y = *+ sinx cos x † Sin X

A:

Q: (e) sin(2x) sin(x) dx.

A: ∫sin2xsinxdx

Q: If y = -cos(2t), then y(5)= ?

A:

Q: 2 sin x f(x) = 2+ cos x find f' (x).

A: use ratio rule for finding the derivative of rational function.

Q: If f(x)- 3 cos 4x- - {).₁ 0 -3 -12 4 find f'

A:

Q: 4)y = 2 sin (3x +) - 1

A: Given: y=2sin3x+π5-1

Q: Let h(y) = 2 cos y – 7 sin y. Then h'(y) =

A:

Q: S (|sin x| + sin æ') dx

A:

Q: 1. sin° x cos x dx

A: sin3x cos4x  = sin(x) sin2(x) cos4(x)  = sin(x) (1 - cos2(x)) cos4(x)  = sin(x) (cos4(x) - cos6(x))…

Q: 2x sin-1(x²)dx =

A: This question is taken from the indefinite integral in which we have to choose the correct option…

Q: e 9. cos(x) dx - " sin(x) dx. Evoluate

A: Formula:∫ cos x dx = sin x + C∫ sin x dx = - cos x + C

Q: 4 sin' 2x cos 4x dx 4.

A:

Q: 3. S sin? (2t) cos³ (2t) dt 4. ſ tan³(3x)dx

A:

Q: Find y' and y". y = cos(x?) y' - -sin (x²) ( 2x) y" =

A:

Q: 1- 2- If x=y√√1-y², find Find y' for y=cos(sin²x) dy dx

A: