S sin(ax)cos(ax)/3 – cos(2ax) dx

Q: O. p. S sin 2x cos 3x dx 3dx /1 + 9x²

A:

Q: π/2 cos² x dx

A: This question can be solved using the concept of properties of definite integrals.

Q: 18) e2x = sin(x + 3y)

A:

Q: (16) cos (xy) find dy/dx

A:

Q: cos 2x 12) S 2cos2x sin x – sin x dx -

A: To integrate:∫cos2x2cos2xsinx-sinxdx Solution: ∫cos2x2cos2xsinx-sinxdx On simplifying further we…

Q: 3r cos(x) 1. Evaluate dx V1+ sin(x)

A:

Q: |3 cos(2x – t/ 2) cos(x+ t/ 4)dx

A: To evaluate the integral: ∫3cos2x-π2cosx+π4dx Solution: We know that, cosa cosb=12cosa+b+cosa-b…

Q: fe²x+Inx² sin x² dx = - +1/√√e²x cos x² dx

A:

Q: fe²x+Inx² sin x² dx = +²√e²x cos x² dx

A:

Q: Find y' : In(cos² 3x) = e*+y + sin-1 y

A:

Q: (d) ƒ sin(1 – x)(2 – cos(1 – x))ª dx

A:

Q: 4 sin x dx (1 + cos x)²

A: Here we have to solve the given integration.

Q: Number 23

A: we have to find definite intregral of given question

Q: S[cos 3(x/3)]dx

A:

Q: If y = cos 3X find dy/dx: y = cos?3x = (cos 3x?. (cos 3x )?. %3D

A: Given, y=cos23x=cos3x2

Q: COSX sin x dx 4. S 1-ఆశి అరికి న

A:

Q: 4. ["s 0 sinx + 2 cos x dx

A:

Q: S(6Vx + 3 cos x - 8)dx

A:

Q: (a) / sin sin(8x) + cos(7.x) dx (b) / (3x – 5 sin dx 2 (c) / cos(3t) + sin(5t) dt

A:

Q: 2x cos x? dx 1+ sin² x² 8

A:

Q: 1. § e sin 4x cos 4x dx 2.5 dx Se-2x dx %3D

A: 1) Given:                ∫esin 4x cos 4x dx Apply u-substitution: u=sin 4x⇒du=4 cos 4x dx…

Q: sin y = cos x (2 cos y– sin²x)

A: Given siny dydx = cosx (2cosy - sin2x)siny dydx -2 cosy cosx = - cosx sin2x…

Q: Take the derivative of this integral.

A: Given

Q: 2 X 1 t3 COS 4- x² dx 2 -2

A:

Q: (4e²+7x°+5 cos z + 2)dx

A: Solve integration

Q: S cos(3x – 2n) cos (x + t) dx

A: We know that, 2cosAcosB=cos(A+B)+cos(A-B) Also, ∫cosxdx=sinx

Q: S 1+cos(3x)dx

A: Given : ∫1+cos3xdx

Q: b) S. cos x cos 7x dx

A:

Q: 2 cos(플x-지) =D v2 TO

A: Given trigonometric equation is:  2 cosπ2x-π=2 We have to solve for x.

Q: d 1. sinx dx = - cos x + C because (- cos x+C) = _ dx

A: The first question is ∫sin(x)dx=-cos(x)+C

Q: 3. fe2x+Inx² sin x² dx = = 2x -+√e²x cos x² dx

A:

Q: x cos x² 2. X C0 dx -siny

A:

Q: 1 dx 3 sin x+4 cos x+3

A:

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

A:

Q: 1. / cos" (2t) sin² (2t) dt

A: 1.

Q: -3π/2 2. S TL √sinx + 1 cos x dx

A: We solve the given definite integral by using substitution method .

Q: 1. x2 cos 2x dx

A: The given integral is: ∫x2cos 2x dx

Q: (d) ſ tan² 3t dt 5 cos? x – 3 tan x dx - (e) S cOs X

A: The integration of the integrals is d) tan2(3t)  e) (5cos2x-3tanx) /cosx

Q: If y=cos (3x+5 ) then the derivative is - 3 sin(/3x+5) 2/3x+5 b) y'=-3sin(/3x+5) V3x+5 a) y'=- c)…

A:

Q: (1) ſ [ (x³ + 2 + 7 ) dx (3) cos³x dx (2) √ x³ (2) x3 e3x+1 dx (4) sin x sin 2x dx

A:

Q: (c) So cos(-x)(x²)dx (d) S(3x² – 2x + 1)sin dx

A:

Q: 1. " x² cos 2x dx

A: (1) We need to evaluate the following integral ∫0πx2cos2xdx

Q: +3x2. Find dy/dx if: (y)² = sin5(cos³(- -)) 2 %3D

A: Given: (y)2=sin5cos3x7+3x22 ----(1) To find: dydx Let u=x7+3x22 , v=cos3u w=sin5v Now equation (1)…

Q: 5 cos(a) sin (x) dx

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

Q: d²s dt2 sin 3t + cos 3t |

A: In this question, we need to find s.

Q: y = cos 3x a. 3 sin 3x b. - sin 3x c. sin 3x d. -3 sin 3x с.

A:

Q: x2 sin3(x) Q.2\ Find dx if y = In cos(x*).V1+x/

A:

Q: 9. (2 sin x – 3 cos x) dx • T/2 - T/2 -

A: We use Trigonometry table for final answer  and cos(-x) = cos(x)  sin(-x) = -sin(x)

Q: dx 3+2 cos x

A: The value of the given integral is 2√5/5 Arctan[√5/5 tan(1/2 x)] + c

Q: (3e + 10 cos(x)) dx ntegral =

A: Integration problem....