Prove that n r=0 "C, sin rx.cos (n-r)x=2"-¹x sin nx. 1

Q: 2FI 2FI sım nx dx = cos nx dx = 0, where n integer. 0.-

A:

Q: sin(2t +) dt = 64 7.

A: Note the formula for the integration by parts : ∫utvtdt=ut∫vtdt-∫dudt∫vtdt .

Q: . Solve for x: 2 cos x + sin x = 2, 0<x < 27.

A:

Q: [6 sin x – 7 sec? x] dx +C - %|

A: Find your answer below

Q: a cos(x²)esin(z²) da -ут 10. TT

A: To find the integral.

Q: Calculate f 6 sinx cos² x dx.

A:

Q: Find for y = 5x sin x+ 10x cos x- 10 sin x. dx Dikdörtg

A:

Q: Let A = {4, 5, 6} and B = {6, 7, 8}, and let S be the "divides" relation from A to B. That is, for…

A:

Q: 18 a Show that / (1 + sin 2zx)dx = n, for all positive integers n. b Sketch y = 1 + sin 27x, and…

A:

Q: sin x cos" п — 1 n 2 2, | co cos"-2 x d.x Show that for cos" x dx Use this to find cos4. x dx.

A: Given, ∫cos4xdx

Q: | sin # da, (h) cos 9 sin 0 de. Ans. (u) 16/I5. (b) 8/10. Evaluate (a)

A: (a). In this part, we use reduction formula to find the value of the given integral. (b). In this…

Q: 3. Find S sin5 x cos* x dx.

A: Use substitution method

Q: 2c. Show that * (5 - ) 4 sin z - cos 2r + 3 -8 cos for every r.

A: To prove: 4sinx-cos2x+3 = 8cos4π4-x2 We know that cosx-y  = cosxcosy+sinxsiny and cos2x= 1-2sin2x

Q: DIFFERENTIATE THE GIVEN y = x² co sec™ 3 -1 * COS

A:

Q: Show that COS x dx a² – x² sin a 2а where a is some positive number.

A:

Q: 9. (1+ sin 0) de

A: To evaluate the given integral

Q: Sinhu.Coshv =1/2 [Sinh (u+ v) + Sinh (u- v)]

A: Sinhu.Coshv =1/2 [Sinh (u+ v) + Sinh (u- v)]

Q: /2 cos x -dx- 1+(sin x)? Compute the integral

A: Consider the following definite integral: ∫0π2cosx1+sinx2dx Substitute sinx=u→cosxdx=du in the above…

Q: General Sol. of  y' tanxsin2y= sin2x+sin2y is

A:

Q: 大 1-cos X P-V= 2

A:

Q: Show that for n ≥ 2, [cos" a da x = Use this to find To cos¹ x dx. sin x cos-1x n + n-1 n I cos"-2₂…

A:

Q: How many solutions exist for sinx cos x = 0 in the interval X € 02 3 5 [0,2x]?

A:

Q: Evaluate f(x) = 7sin r 1 COS -X %3D at a /3. x =

A: Given fx=7sinx-cos12x To evaluate the value of function at x=π3 put this value in fx fx=7sinx-cos12x

Q: Use the double-angle formula cos 2x = 2 cos x – 1 to evaluate the integral 1 1+ cos 2x dx

A: The given integral is ∫11+cos2xdx

Q: Find dx 11 for y = 9x2 sin x + 18x cos x – 18 sin x. dx

A: Finding the derivative of y

Q: 4 6 (1+ tan? z) dr = 0.

A: Use identity then solve

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

A: