VE- -I Cos a dx is equal to O 2Va – a cos a + C O 2VI - a sin a + C O VT - x cos a + C O 2Va - cos ax + C

Q: sin(e)de 4+cos (e) In(4+cos'(e)) +c -sinh -sinh cos (0) sinh (cos (0)) +c 2/4+cos (0)

A: Use the substitution method and integrate the given expression.

Q: 32. y" + y = sec x; y = c1 cos x + c2 sin x + x sin x + (cos x) In(cos x), (-7/2, T/2)

A:

Q: x/4 The definite integral sin24x cos2x dx is equivalent to x/2 1 -sin20 cos20 de A x12 2sin20 cos40…

A:

Q: The appropriate trigonometric substitution that solves the integral SV5 + 4x – x2 dx - A) x = 2 + 3…

A:

Q: sin x P47. Let I = cos.x dx and J = J% sin x+cos dx, a e [0, ). sin x+cos x (a) By considering I+J…

A:

Q: Use integration by parts to evaluate 2x cos (x) dx -x?cos (x) +c - 2x cos (x) + 2sin(x) +c x?sin (x)…

A:

Q: Evaluate: /sin(/x)dx A 2/x sin(x)-2cos(/x)+C B2/xsin(/x)+2cos(/x)+C 2sin(/x)+2/xcos(/x)+ C D…

A:

Q: 2х dx cos?(2x) Evaluate 1. xtan (2x) + In|cos(2x)| + C 1 xtan (2x) + In|sec(2x)} + C xtan (2x) 1…

A:

Q: sin30 de 10. J 1-cos e 11. J sin 20 sin 40 de. cos?30 d0 12. S 1 -cot 30 13. J tan 50 d0. 14. S csc2…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: e interval 0, 2T). Approximate the solut 6. cos x(coS +2) 1 11

A: Consider the provided equation and simplify:

Q: a Find the values of A and B in the identity A (2 sin x + cos x) + B (2 cos x sin x) = 7 sin x + 11…

A:

Q: Įsin x cos^(3/2) x dx * O -2/5 cos^(5/2) x + C O None of the choices -5/2 cos^(5/2) x + C O -2…

A:

Q: x + sinx dx. Evaluate: 2x- cos/x (A + C 2 2x+ cos/x B + C 2 © x-2cos/x + C x +2cosx+ C E None of the…

A: Let √x=t then solve it.

Q: N! sin(B t) s2 + B2 cos(B 1) s2 + B2 N! (s - A)N+1 B A sin(B t) (s - A)? + B2 S - A Ai cos( B t) (s…

A:

Q: ſcos (x/2) cos (x/3) dx * 3/5 sin(x/6) + 3 sin(5x/6) + C None of the choices 3/5 sin(5x/6) + 3…

A:

Q: sin [cot(4e¬4*)]cos*[cot(4e¬4*)] dx e^x sin²(4e¬4x) Let u = cot(4e¬4x) %3D

A: Solution: Let the given integral is I=∫sin6cot4e-4xcos4cot4e-4xdxe4xsin24e-4x ......(1) Substitute…

Q: f (x) = 3 sin x + 3 cos x, [0, 27]

A: Consider the function: fx=3sinx+3cosx Differentiate the given function with respect to “x” then,…

Q: (1+sinx)9 cos x dx , u=1+sinx is The values of a. (1+sinx) 10 + C 10 b. (1+sinx)10+ c 1 (sinx)10+c…

A: Solution: The objective is to find the value of the given integral

Q: Use integration by parts to evaluate 2x cos (x) dx (A А -x?cos (x) +c B - 2x cos (x) + 2sin (x) +c…

A:

Q: a) _*? (1-x²)Z x+3 b) S- x2+2x+5 c) Find the value of sin(tan-1- sec-d) dx d) S x² Vx2+1 e) S Vx2+2x…

A:

Q: Sin x 10. y = 2+Cos x 3 2+Cos x Ob. (2+Cos x)? Cos x C. (1+Cos x)2 1+2 Cos x d. (2+Cos x)? Oa.…

A:

Q: Assuming that y is a function of x, then - (cos(x²)] = -2x sin(x²). dx Assuming that y is a function…

A: Use chain rule of differentiation to differentiate composite functions. ddxfgx=f'gx⋅ddxgx

Q: sin-1x If y = dy cos(t) dt, then dx Select one: a. cos(sin-1x) b. X /1-x² c. Non of them d. 1 e. 1…

A:

Q: 7/2 0² sin 20 d0

A:

Q: sin?x If h (x) = | . (t² + 1) dt for – <x < 7, then h' (x) CSC 4 (A (a4 + 1) CSC B) (sinºr + 1) CSC…

A: Let's find.

Q: cos x 4. Compute the integral 1+(sin x)? Hint: u-substitution

A: the given expression is: ∫0π2cosx1+sinx2dx let the given integral be I. therefore,…

Q: cos(x) dx = dx. Use - 0o (1+x²)² o cos(x) 00 cos (x) Compute Jo 1+x²)² dx. Note that 2 (1+x2)2 the…

A:

Q: cos(z) b) O f'(x) 1+ a? cos(r c) O f (x) Vi - 2² d) O f (x) = 1+ cos2(x) cos(x) 1 + sin (z) e) O…

A:

Q: 2.5 1 –dx 1+ sin x – cosx COS X 1

A: Solution

Q: see the question as attached here with this uppload.

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

Q: [ sin(mx) cos(nx) dx- D Suppose m and n are constants and m #n. Evaluate 1 1 A -cos(m-n)x- =…

A: This question can be solved using the concept of integration of trigonometric functions.

Q: tan x.cos xr =D1 (p) X UIS sin? 0+sin? 0. tan? 0 = tan? 0 (1) 2 %3D 1- cos 0 cos? 0 + 2 cos 0+1 1+…

A: Since you have posted multiple subparts we solve first three subparts  for you To get the solution…

Q: 8. (sin e - 2r cos e) dr +r cos e (2r sin e +1) de =0 9. (w³+wz² – z) dw + (z² +w°z– w) dz = 0 10.…

A:

Q: 16 sin?x 5. The integral S dx is equal to (useful identity double angle identity for sin) cot2 x+1 1…

A:

Q: Q.3 Use ODE methods to solve the BVP: U = 18xy + sin(2x- y) U(0, y) = y -cos y, U(x,0) = x² -cos2x,…

A:

Q: Cos ax COs ax Q: Prove that dx = ze", a 2 0.(or) Evaluate x² +1 x² +1

A:

Q: 2 a sin 0 0 a²_r² .2 a So 0 rdz dr de

A:

Q: O 1:0: d (sin-x?) = (sin-1; dx 1 d V1 - x² dr (x²) خيار 4 1 V1- x4 2x V1-x2

A:

Q: (d) r(π/6 + At) - r(π/6) = √3 2 cos At sin Ar-1+(cos Ar i+ At + 2 3√3 2 -sin At 1 3/-)1 2 X

A: We can solve as follows

Q: 1. (a) Use integration by parts to verify the reduction formula l(cos"-² x dx cos"- xsin x, n–1…

A: Solution:Verify the reduction formula∫cosnx dx=cosn-1x sin xn+n-1n∫cosn-2 x dxDerive the Wallis…

Q: 4 sin? x cos? x dx. sin(2.x) cos(2.r) Evaluate the integral (a) In |sec(2a)|+C (c) In |sec(2x) +…

A:

Q: fe* cos (2x) dx A. B. C. D. 2e* sin(x) + 2e* cos(x) + C 2 2 ex sin(x) ex cos(x) 2 2 2 ex sin(2x) ex…

A:

Q: 6secx cos x dx is O a. 6x + c Ob. O b. 6 sec x+ c O C. 6 sin x+c O d. - 6 secx +c

A: Given ∫6secx cosx dx

Q: (7-cos"(x) cos(x) sin(x) e dx = A) 7 ese(x) +esla(x) +C B) 7 sin(x) -x+etincx) + C C) other

A:

Q: Q No 3.Evaluate (a) S - (1-cosx}idx (cosz(1+cosx)(2+cosz)jå (b) S **(cos"i 3=)*dx Vi-92

A:

Q: sin If y = , then justify (1–x² )n. -(2n +1)xy, – n² y,-1 =0 applying Leibnitz's a) theorem.

A: Please check step 2 for the solution.

Q: sin 5x sin adx =? O A, sin 4x sin 6x +c 6 4 sin 4x sin 6x OB. 8. +c 12 O C cos 4x 8 cos 6z +c 12 O D…

A:

Q: The auxiliary roots of the auxiliary equation associated with a certain HLDE are m= ±3, ± 3i, ±3i.…

A: Given auxiliary roots are 3,-3,3i,-3i,3i and -3i

Q: sin³ydy 1+ cosy A 1+ cosy В 1- cosy siny D sin³y E) None

A:

Q: |2tan x In (cos x) dx= A sin x [In(cos x)] + C (B cos x [In(cos x)] + C В C [In(sinx)]? + C D…

A: