1 cos(5x) +... 25 cos(x) + cos(3x) + Ans. + 2 sin(x)+ sin(3x) +sin(5x) +...

Q: COS (+3 O cos x Ocos 2x O sin a Ocos z +x) + cos (-) is equivalent to:

A:

Q: 1. (2x4-x3-2x+3) dx 2. (3-2x)2 dx 3. 3(x-1)(2-3x) dx 4. (5-5x+x5) dx 5. 1/3 ex dx 6. (x2-cos x)…

A: The integration is an anti derivative process. it is reverse of the process of differentiation. Here…

Q: 4. Solve cos x = cos 2x for the interval x E

A:

Q: (b) (cos(x) (2x + 3))'

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

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Q: + 5x + 6 cos x + 2)dx = e – x + cos a + 2 + c - O 3e* + x³ + 6 cos x + 2x + c 3et + x + 6 sin x + 2x…

A: We need to evaluate the following integral I = ∫3ex+5x4+6cosx+2dx

Q: 4 Se + 5x* + 10 cos x + 2)dx 5e" + x° + 10 sin x + 2x + c 5et + x 10 sin x + 2+c - et x° + cos x + 2…

A:

Q: 1 - cos 4x 1 + cos x dx

A: The given integral,     ∫1-cos4x1+cosxdx

Q: sinx S- cos?x+ 6cosx+13 O In cosx+3-Vcos²x+6cosx+13|+C O In cosx+3+/cos²x+6cosx+ 13 O…

A: To find:

Q: The f cos 5x cos x dx is 1 {A} = sin 4x - 12 1 1 {B} sin 4x + - 8 12 cos 6x + C cos 6x + C {C} {D}…

A: Given problem:-

Q: 4. The value of fx sin(x²+3) dx Acos (x²+) + C C. cos (x²+)+C B. -cos (x²+)+C D. -cos (x²+) + C

A:

Q: [-7, 1] The average value of cos (2z)e1-sin(2z) on is

A: The average value of the function f(z) on the interval a, b is  1b-a∫abf(z) dz.

Q: y = sin' x- cos 3 – cos' x cos³

A:

Q: 6. Suppose you wish to differentiate g(x) = sin²(x)+cos²(x). What is the fastest way to do this, and…

A: Given,

Q: 2. Vsin 3x cos 3xdx

A: Given: I=∫sin3xcos53xdx For evaluating given integral, we substitute sin3x=t…

Q: f cos(x³) x² dx. O 1 ¹ cos4 + c 4 1 3 sin x²+ C 1 1 ¹ cos4 + c - 4 -3 si sin x³+ C

A:

Q: coS x dx 6) 1 + 3 sin x A) In| 1+3 sin x|+C C - 를 In| 1 +3 sin x| +C

A: To evaluate ∫cosx1+3sinxdx

Q: (11) y" +3y' – 2y = e-2"[(20x + 4) cos 3x + (-32.x + 26) sin 3.x] (12) y" + 9y = sin 3.x + cos 2.x

A: We are entitled to solve only one ques at a time and up to 3 subparts only. Given - y'' + 3y' - 2y =…

Q: (4) Evaluate cos (2x) -dx. (x² + 1)² 8.

A: If y=f(x), then the independent variable x is called the input of the function and the dependent…

Q: 6. Evaluate A sin³ x cos4 x dx.

A:

Q: Using appropriate substitution, sin³ (3x)cos*(3x)dx is equal to -cos"(3x) + cos"(3x) + c - cos (3x)…

A:

Q: y = x cos(In x)+x² In x²

A: d dx(cosx) = -sinxddx(lnx) = 1xddxx2 = 2x   Product rule u.v = u'.v + v'.u

Q: 3. Express 1++cos2x in terms of cos x. hence a. Evaluate (1+ cosx)dx b. Express 1- cos2x in terms of…

A:

Q: 1. y = In (3 – 4 cos x) + (4x – 5)5

A: 1). Given function is y=ln3-4cosx+4x-55. To find: dydx Solution: Power rule of differentiation…

Q: 2. Evaluate: S(cos x)(In sin x)dx A. sin x (1 – In sin x) + C C. sin x(In sin x – 1)

A:

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

A:

Q: 2 cos (x2) - 4x 2 sin (x2)

A: 2 cos (x2) - 4x 2 sin (x2)

Q: Find the Solution of differenthial Cos X

A:

Q: 3. у"-2у'— sin 4x 1 cos 4x 40 1 sin 4x 20 Ans. y= c, + c,e²* + -

A: To find: The general solution of differential equation. Given: The differential equation is…

Q: cos 4x cos 2.xdx 3.

A:

Q: - 3in 2 X sin X- COSX

A:

Q: Given In = S cos" x dx = - cos"-1 x sin x + In-2 ; %3D n/2 determine a reduction formula for cos" x…

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Q: 1 os( 1 (sin(7z))* =| x)+ cos( x)

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Q: 14. Evaluate cos 3x+ dx. 2

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Q: 1. Solve the DE: (cos y- cos x)y' +cos y sin 2x = 0

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Q: 3. fe2x+Inx² sin x² dx = = 2x -+√e²x cos x² dx

A:

Q: For | cos 3x cos 4x dx :

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Q: 4. Find all solutions to the equation 4sin x cos x = v2 in the interval [0,2]

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Q: 1-Let :=x+iy then cosh(iz ) is equal to a-cos' y+ sinh' x b-cosh' y-sin'x e- sin' x+ sinh v d- None…

A: Let z=x+iy therefore, iz=ix+i2y=ix-y=-y+ix we know that  coshz=ez+e-z2 therefore, cosh…

Q: 12) f)=sin(x) 0<x<1 Ans. 24 1 (₁ A 7 (1)(3) 1 -cos(2x) +- -cos(4x) (3)(5)

A:

Q: 1 3 X° cos 4- x2 dx + 2 2

A: We will find the value of definite integral as following.

Q: 7. Over the domain 0s x s2n, the equation cos(x)-sin(x)%3D2 cos(2x) has:

A: We find the solution in the following way by using trig identities.

Q: 2. cos(4x) = 1 – 8(sin(x))²(cos(x))²

A:

Q: Evaluate D°(cos x +e-2") A cos x – 32e-2x (B) sin x + 64e -2x (c) - sin x – 32e -2r (D - cos x +64e…

A: Here we have to evaluate      D6(cosx+e-2x)

Q: Determine the general solution of: a) -3 sin x = cos 2x b) cos 2x =1-2 cos x ||

A:

Q: 4. f(x) = 2 cos(x – 2n)

A: Given:  f(x)=2cos(x-2π)

Q: dy.xandy in =cos = COS e

A:

Q: + 5x* + 4 cos x)dx = et – x° + cos x + c et + x 4 sin x + c - 4e" + x° + 4 cos x + c ,5 4e" + x° + 4…

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Q: 1. Solve cos 2x - 2 sinx - cos*x = -3 on the interval x e [0,21).

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Q: n3xcsC3X)ax 3. S sin2xcsc3x+cos²xcsc3x

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…