Verify. esc (x) [I-cos(2x)] = 2 sin (x) SC

Q: 2. cos?x dx =x+ sin 2x + C X_SO

A:

Q: sin in dx X COS21nx

A: A detailed solution is given below.

Q: What does the following identity tell us about the derivatives of sin -1x and cos- 1 x?…

A: Explanation: Suppose that,  A=sin-1xB=cos-1x   Now we can say that,  sinA=xsinB=x  So,  x=sinA=sinB…

Q: Evaluate: 2x +tan 2x 1/3 COS ,2 1+x? 1-x2 dx. e* +1 -1/3

A:

Q: Graph the function ƒ(x) = sin 2x + cos 3x.

A:

Q: f(x) = (8 sin x + 3 cos x)tan1 -

A:

Q: Use the substitution rule and show all the steps to evaluate: 1 dx 1+ sin x – cos x

A: ∫π3π2 11+sinx-cosx dx Apply u substitution u=tanx2 find derivative of u with respect to x…

Q: is a root of the equation y2 + ycot x cos x - 1 = 0

A: Here we have to show that, y = sin x is a root of the equation y2 + ycot x cos x - 1 = 0

Q: Evaluate L. Cos 3 -1 X x² + 1 dx

A: Simpson's 13 rule: ∫abydx=h3(y0+4(y1+y3+y5+...++yn-1)+2(y2+y4+y6+...+yn-2)+yn), where h=b-aN and N…

Q: 23. x? sin (x³) cos (x³) dx

A: ∫x2sin5x3cos3x3dx=∫sin5x3cos3x3dx      x3=u,3x2dx=dx, x2dx=1/3 dx=∫sin5x3cos313dx

Q: Evaluate √x² cos (2³) de dx

A: The given integral is: I=∫x2cosx3dx    ...1   As we know the common integral. ∫cosxdx=sinx+C And…

Q: . Eliminate all the arbitrary constants in the equation as follows: y = Ae2x- e-5x (B cos 2x + C sin…

A:

Q: Using (11) and (12): 1 dx 1+ cos x tan +c

A:

Q: Sx2.- cos³ x-5 du 1-sin? x

A: Evaluation of the integral, bu using integral by parts

Q: B) Express the given quantity in terms of sin x and cos x sin (플-x)

A:

Q: (40 sin (x) – 39 cos (x)) dx =

A:

Q: Evaluate: * cos² 2. * x cos? x dx sin

A: Given: ∫cos2xsin4xdx

Q: (d) (sin(x + cos(2x + 3√)))'

A:

Q: Evaluate ∫ a cos x dx and ∫ a sin x dx, where a is a constant.

A: Given∫a cos x dx

Q: 4. Describe a way of evaluating x cos? x dx. sin' х. х со

A: We will use the reduction formula,  to solve this integral. where n ≥  is an integer. Now., we…

Q: Q: Evaluate: 2х -1 cos dx (1+x²

A: Solved below

Q: Ly = Ce* + C2 cos x + C3 sinx

A:

Q: How do you solve this and can you show me step by step?

A: Given equation is

Q: 2T Rewrite cos x + 3 in terms of sin(x) and cos(x)

A:

Q: d(tan(x)) Using Euler’ formula, show that dx cos x 1.

A:

Q: a) ㅠ 3 cos x sinx dx

A:

Q: In cof '3x sinAte ech x² 2

A:

Q: - sin(x®) 9u e cos(3x)· du 9u? Inx5

A: Given- ∫lnx5sin(x6)cos(3x)e9u29u2du To evaluate the given integral.

Q: Se2* (sin x + cos x)dx

A:

Q: sin(플 + 2x) %3D cos(플 - y) 2- Which of the following is the relationship between x and y according…

A:

Q: Evaluate o (3 sin x – 5 cos x) dx.

A:

Q: 1. cos x |? ecosx sin xdx

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: у 3 3x? sin "(2x)+ 2х

A:

Q: Q/ solve the differentil-equation ty-f'sinx-x)+(3xy+2y.cosx)

A: We will solve the problem.

Q: 4. COS dx sin?

A:

Q: Express the given quantity in terms of sin x or cos x. sin (6t – x) O A. cosx- sin x O B. - sinx C.…

A: The given expression sin6π-x

Q: e'sinx y.cosx

A:

Q: y = sin x cos6x x CO

A: Introduction :

Q: 3*x? f(x) = sin (3x)

A:

Q: (b) cos x = 0.549

A:

Q: Evaluate sin z -dx /4 - coS I

A: Use the substitution method and first simplify the integration than integrate.

Q: cos (4x) dx 1+ sin? (4x)

A:

Q: Evaluate: [e* 1+ sin 2x dx 1+ cos 2x

A: Topic:- Integration

Q: 17. Determine the equation f(x) = cosx as a sin function.

A:

Q: Evaluate and simplify y′. y = 2x2 cos-1 x + sin-1 x

A: Given:y=2x2 cos-1x+sin-1x

Q: dx It sin x-cos x COS

A: To evaluate:∫dx1+sinx-cosx Solution: We know,cos2x=1-tan2x1+tan2x     ...(1)sin2x=2tanx1+tan2x…

Q: | cos(x) sin(2x) dæ

A:

Q: 3 Evaluate COs x sin æ dx. sin*(x) X + C

A: