E(- 1y**cos(nx) n=1

Q: 2 sin 2x dx Vcos4 x + 4 cos² x – 2.

A: Given that, ∫2sin2xcos4x+4cos2x-2dx The trigonometry equation is, sin2x=2sinxcosx Take…

Q: S 4- e-2) cos(e- + In z) dz

A:

Q: Determine of y = cos(x) – V5a2 In x.

A: I have stated the used formulas in the solution.

Q: |2tan x In (cos x) dx=

A:

Q: a 1 - x²) cos(nx) dx F(x 一九 4 sin(nл) — 4nл соs(nл) — 2n²л² sin(n) πη3

A:

Q: 1. Integrate: e3x cos(x) dx

A:

Q: 2tan x In (cos x) dx=

A: here we have to integrate the given integral.

Q: 4. If y3 +x³ = sin y + sin x find. dx 3y²-cosy А. cos x-3x2 3y2-cos y В. - cos x-3x2 cos x-3x2 C.…

A: Given: y3+x3=siny+sinx To find: dydx=?

Q: 3+9sin' x Evaluate dx using suitable technique. cos x

A:

Q: 1-[t2 cos at

A:

Q: - / sin 8x cos 5x dx = 1/6 cos3x + 1/26 cos13x + C ) -1/6 cos3x + 1/26 cos13x + C ) -1/6 cos3x -…

A:

Q: [ 2x sin (4x)dx O =cos (4x) + C -x² 4 2 sin (4x) + 8x cos (4x) + C sin (4x) – x cos (4x) + C ○중cos…

A: Integration by parts

Q: establish each identity.

A: Given  The identity is ln sec θ=-ln cos θ

Q: Sf(x) dx = 1 0.694 (sin(x) dx = 1 0.694 COS TX T C = 2 C 0.694 How? ==→ 1-C05 (0.69471) = 1694 -

A: To determine the value of C .

Q: The value of integral (cos(4x)+cos(81)) dx

A: We have to determine the integral

Q: Assuming In = [ cos" xdx. and n > 2: 1 п -1 n-1 r sin x + -In-2; CoS' In n %3D n

A:

Q: 16. If 2 sin 2x s 3 cos2x and 0s 2x then x=

A: Given : if 2sin2x = 3cos2x and 0≤2x≤π2 . then we have to find the value of x.

Q: 2. 1- x2dx cos(x + 1) dx 3.

A:

Q: 11 Evaluate ff sin(y²)dydx where 2: 0<y <1, 0<x<y°. 0x a) 1-cos(x) b) (-cos(x)) --cos(1) d). cos(1)…

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Q: 4) f(x)=- - T <x< T Ans. 4 cos(x) +cos(2.x) - 4 cos(3x) +... 12

A:

Q: Find the indefinite integral ∫cos 2x cos 6x dx

A: Given integration as I=∫cos 2x cos 6x dx Since  2cos 2x cos 6x=cos 6x+2x+cos 6x-2x…

Q: Compute*cos(Inx)dx. 1 A.-—-e (cos1-sin1) - 2 2 1 B.- e 1 C.-e TT 1 2 e

A:

Q: INTERGRATE THE FOLLOWING: -0.33 (1). S [8.5244 x 10 (1 – cos(4.759x)] dx ,0.33 (2). [8.5244 x…

A: It is an Integration problem. I used substitution method to solve the second question. I  evaluated…

Q: (d) lim In(cos r) エ→0

A:

Q: 3x cos 8x dx e3x e3x A) [8 sin 8x - 3 cos 8x] + C B) [8 sin 8x + 3 cos 8x] + C C) (8 e3x sin 8x + 3…

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

Q: dx+ 1.5 +§ (5r – 15)cos (5х — 15)сos dx COS 1.5 Jo (5x)cos 1.5

A: We have to apply the integral by parts.

Q: integral cos^7(4x)

A: To find the integral

Q: 7 sin(x) -dx 2 cos x+5cos(x)– 3 4.

A:

Q: Find y' (y prime) and y" (double prime)y = cos(x2)

A: To determine the expressions for the first and second derivatives of the given composite function

Q: 17. If 4 sin x+3 0 on 0 sx < 211, then x=

A: We have to find x if 4 sin x+3=0 on 0≤x≤2π. Solving the given trigonometric equation, 4 sin x+3=04…

Q: (e²)(sin²2x) Compute In y and In 5z

A: Basic log formula are applied to solve the question.

Q: too ·00 dx COSX x² +hx+5 =le Residue solution cos (2)

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Q: f(x) = cos (In (3x))

A:

Q: 3. Prove that: cosh x - sinh x = e¯*

A: Proved Coshx - Sinhx = e-x

Q: 11. y = x² sin x + 2x cos x – 2 sin x 12. y = x² cos x 2x sin x – 2 cos x - -

A:

Q: In(1+cos 3x) +C dx 3. 1+cos 3.x

A: Differentiate of the RHS the we get RHS

Q: sin(6x) cos(4x)dx% = %3D (b) ÷( + ) Nin (6x) cos (2x) COR +c 2. 2)+ (e) None Cos (2x) Cos (10x sin…

A:

Q: 4. [(3sin 2f – 3 cos 5t )dt 5. sin x dx cos x

A: 4) Given:            ∫3sin2t-3cos5tdt       =∫3sin2t dt-∫3cos5t dt taking constant out…

Q: Show that d 1 In cos(x) os(x) - csc(x) dx 1+ cos(x

A: We have to proof

Q: Find 2 if x? cos4 cos* T. 1) 2xcos x+4x2cos3xsinx 2) 2xcos x- 4x²cos³xsinx O3) 2xsinx sin xcosx 4)…

A: Hence option (2) is correct.

Q: 1. f/² sin (1) cos (4) Sir sin (²) dx (Consider initially the first 2 terms)

A:

Q: Find L{(t- 2) (3 cos 5t + 1)}. COS 3(s2-25) (s²+25)? 30 | s2 s2 +25 6. 3 g3 s2 s2 +25 s(s² +25) 6s…

A: Find the Laplace transform of  L{(t-2)(3cos5t+1)}

Q: Evaluate /(e* + - + cos4x)dx O + logx + sn3x +c e2r 3 4 e3x sin4x + logx + + c 3 2 O + logx + e5x 2…

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Q: 4) Find when y2 – x² + cos(x + y) = 0

A:

Q: find y prime and y double primey=cos(x^2)

A: To apply chain rule and product rule to find the first and second derivatives of a composite…

Q: 7/2 in° x cos' xr dx 4

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Q: dy.xandy in =cos = COS e

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)