3nt 3nt s = sin 2 + cos 2 %3D

Q: S .2 4. sin x cosx dx

A:

Q: 10. (2 sin x + 3cos 2x)dx

A: As the policy of bartleby the provisions is to solve only one question at a time when

Q: 1 S cos³ 3x sin' 3x dx

A: The given integral is: I=∫cos33xsin43xdx   ...1   We know that; The Power rule: ∫xndx=xn+1n+1+C

Q: 1. sin " 2xcos' 2x dx

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: (b) ſ sin³(x) -dr cos (1)

A: Let's solve given integration.

Q: 6. S 2sin´x sin(2x) dx

A:

Q: S sin5 3 x cos' 3 xdx

A:

Q: S 5 sin(3x)e2cos(3r)dx

A: Solve integral by substitution method:-

Q: i) Find sin 6x+ cos 4x dx. 3 ii) Evaluate || et -dx . Hence, solve 2e* dx . (* +2)" +2

A:

Q: 7/2 S 3 cos (x) sin°(æ) dx =

A:

Q: (3 S sin xdx

A: Note: "Since you have asked multiple questions, we will solve the first question for you. If you…

Q: 2. S(cos4x – sin*x) dx

A: we know that , a 2 - b 2 = ( a + b ) ( a - b ) And cos( 2x ) = cos 2 (x) - sin 2 (x )

Q: Evaluate the integral

A: Let the given integral be y - y = ∫6sin2x1+cos4xdxy = 6∫sin(2x)1+cos2x2dx…

Q: 6e(6 sin 3x) dx sec 3x

A: Inverse of sec3x is cos3x Cos3x=(1/Sec3x) Putting in the integration problem

Q: S cos 4x cos 3x dx

A: We need to evaluate integral.

Q: 7. S (x-1+cosx) cos2(sinx+lnx)

A: We use substitution method to solve this integration

Q: 2TT Sin nx dx

A:

Q: 9. S sin(4x – 2) dx

A:

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

A:

Q: S sin5x cos³x dx

A: Given∫sin5xcos3xdx

Q: ∫cos(3t)sin(8t)dt

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: 1 dx 6- cos²xsin²x

A: use trigonometric identity to prove the integral

Q: (2) S sin6 x+cos6 x sin³ x cos³ x dx

A: See this solution in below.

Q: 4. ſ cos xesinx dx

A:

Q: 4. f cos? 2x 4. cos? 2x sin 2x dx 2 2 5. f sin¹¹ ²3x cos / x 3x dx

A:

Q: 3. S sin³ 0 cos³ 0 d0

A: Given

Q: (#5) ſ cos³ (x)sin*(x)dx =

A: Given the function,

Q: y = sin(3x) + cos(0.5x)

A: Given: y=sin(3*x)+cos(0.5*x) We have to determine the value of y,where x varies from 0 to 2pi in an…

Q: )S sin cos5 x dx

A: Solve the following integral

Q: 3 1. cos x - 5 dx -3

A: The given integral is ∫-34 cosx-3x5dx. Evaluate as follows.

Q: ²e²¹ sin(3x) dx, n=8

A:

Q: 5. (1+ cos 3x ) dx

A:

Q: 2 sin x cos8x dx

A: Given- ∫0π2sin6xcos8xdx To Find- The value of the above integral. Identity Used- The value of the…

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: -3π/2 2. S TL √sinx + 1 cos x dx

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

Q: ∫cos^4 2x dx

A: Please see the answer in step 2

Q: S 4 cos (x) sin (x) dx = %3D

A:

Q: 3a. cos πx sin πχ dx

A: We need to integrate the given expression. ( As per our policy, we can solve 1 question at a time.…

Q: 24 dx 1- cos (6x)

A:

Q: 4. sin+ cosx – 1 = 0 (L3)

A: Solution of problem (L3) 4

Q: 1. " x² cos 2x dx

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

Q: (1) S cos(7x + 5)dx

A: We need to integrate the given terms.  For this we will use substitution method.

Q: 1. S 2x sin-1 x? dx.

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: * /2 2 sinh (sin 0) cos 0 d0

A:

Q: 9) S 2 cot 2x cos x dx

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 5. S sin(3x)dx (a) 3cos(3x)+ C (b) †cos(3x)+ C (c) – 3cos(3x)+ C

A:

Q: 6sin³ (2x) cos(2x) dx =

A: the given indefinite integral is: ∫6sin52xcos2xdx we have to find the value of the given indefinite…

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.