e Cos 5. J1-x2 -1 COS

Q: 7 sin°(e) cos"(t) dt

A: To evaluate the given definite integral

Q: f (t) = t(e-2t + cos at)

A:

Q: 14-f(t)= cos 2t.

A:

Q: 2e cos 2t

A: Given,       2elncos2t

Q: f (t) = e(-3t) sin(2t) cos(3t) cosh(t)

A:

Q: Q. It sin x Cos X XCOS xQ /- sin xd 3.

A:

Q: cos e de V1 – sin 0

A:

Q: cos e de =. 0. От O -T O 3 O 6

A:

Q: T Cos x-sin x Jr x² dx So

A:

Q: 37/2 8 cos x dx T/2

A:

Q: 10. f sin x dx 25+cos²x

A:

Q: Evaluate L{t°e! e3(1 – t) 3e-t sin (4t - 2) 2) + t2 $ (3t)} cos

A: Explanation of the answer is as follows

Q: S*r(sin³x cos x + sin x cos x) dx -- 4 Ja sin 50 de

A:

Q: 2. Evaluate (x2 – 1)e" dx T/2 3. Evaluate cos (0) d0. Write your ans"

A: Consider the integral- I=∫01(x2-1)exdx =∫01x2exdx-∫01exdxLet I=I1-I2—(1)Where ,I1=∫01x2exdx and…

Q: d 1. Find (esin(x)+cos(æ)) dx

A:

Q: T/2 cos t dt 1 + sin²t

A:

Q: dx 2. S; 3 cos x+4 sin x

A:

Q: (b) I cos cos(√x + 3) dx

A: b Given integral is ∫cosx+3dx. We have to solve the given integral. Use formula…

Q: Q: Evaluate: 2х -1 cos dx (1+x²

A: Solved below

Q: L(cos at) = s2 - a2

A: To verify that ℒcos at=ss2-a2.

Q: 2. f(t) =t cos 81 +2

A:

Q: Differentiate: y = cos(5 e* ) e11 COS

A: Ans is. option a)

Q: 4 sin"t- cos *t= sint- cos 4 2 2

A:

Q: evaluate the triple iterated integral.

A:

Q: cos E(z) = 2. e of order e of order e of order

A:

Q: 2. Find cos ec (In x) dx . x1+ cot(h x)

A:

Q: (a) L{t+ sin 4t – e cosh nt} -

A: As per our guidelines, we are supposed to solve only first question.

Q: 3. Evaluate L{4e-2tt3 +t sint cos t}

A: L4e-2tt3+t sint cost

Q: Q/ solve the differentil-equation ty-f'sinx-x)+(3xy+2y.cosx)

A: We will solve the problem.

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

A:

Q: dx 3. S. 5sin x+12 cos x

A:

Q: .2. COS X sın.x.ços.Xdx

A:

Q: cos e de =_ %3D • 2 • -T • 6

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

Q: 4 + cos t -dt 1 – sin t

A:

Q: (z*sin - 2° cos 2y cos r2 y? dr+2xy cos ,dy = 0.

A:

Q: The antiderivative of Cos(3x)

A:

Q: Find Lt+1)²-e' sin² t + cos(t+1 ++ π)}.

A: Given :

Q: tegral 1 -r³e"la0 cos²e ,² dr sin@d0 ¢ do = x 32πα x = ? %3D

A:

Q: 5. (y" – y) = e-X cos(3x) %3D

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

Q: /2 | cos(r)e sin z dx O a. el O b. e sin 1 C. 1—е 1 O d. cos 1

A:

Q: (ii) Evaluate J dx. COS TI

A:

Q: 3 cos(wt - a), where w and a are constants

A: We find the Laplace transform

Q: f(8,t) = cos os(0e*) + cos( + e*) = COS + cos (s+

A: Find partial derivative.

Q: (5e" + 6x + 5 cos z)da

A: The solution is given below

Q: 6. J1-cos I COS T dx

A: Answer is mentioned below

Q: 2 cos e de 2 V1 – sin 0

A:

Q: 1. Evaluate 9/ COS x (a) (1 – x)e dx (b) ,"™ dx p) A-2 sin r -

A:

Q: Find dg(t)/dt 1+ cos t -1 8 (1) = sin t

A: