[t5 ] = ? %3D 120 24 s6 O A D QI L[(t+ 1)?e] = ? 24 120 s5 Oc B s2 + 1 s2-1 L [sin? (t) + cos?(t)] = ? (s – 1)2 (s-1)2 %3D 1 B O 4 ja s2+12 s2 -1 O B O D s2+1 (s+1)² (s+1)² 1 s2+12 s5 O c

Q: 17 3 sin x-4 coS X

A: Solution 17. Given integral is  ∫13sinx-4cosxdx. Now, 3sinx-4cosx=6 tanx21+tan2x2-4 1-tan2x21+tan2x2…

Q: Part 1: 1 1. S *(In x)3 dx 2. Se3x cos x dx 3. S(1 + x²)e-*dx 4. So x²e*dx

A:

Q: (b) J 32+3 22²-2-1 dx

A:

Q: 1 Laplace transforms Calculate the Laplace transforms of (i) H₂(t) cosh (3t), where cosh (at) = 1/²…

A: Solution: (i) let, f(t) = H2(t)cosh(3t)                   = H2(t)[(1/2)(e3t + e-3t)]…

Q: y=Sin x -37 30 Ly= cos x - 37 -2 77 ST 377 2. HN - 15

A: Answer is mentioned below

Q: 8. Evaluate: ſ V1– cosx dx A. V2 cosx + C c-2 sin를 + C B.-VZCOS를 +C D. -VZcos + C

A:

Q: Solve the equation: (D² - 1) y = 0 Oy=c₁e* + c₂xe* + c3 cos x + c4 sinx Oy=c₁e¹* + c₂e + c3 cos x +…

A: A detailed solution is given below.

Q: cos 2x dx (b) 4 cos t dt 0 2

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: L' (s²+4)(s²+9) 3 f cos(2a) sin[3(t – æ)]dx O b) cos(2t) sin(3t) c) None of these 1 * Só cos (2a)…

A:

Q: L{t sin t cos t} = 2s (A) (s²+4)2 -2s (B) (s²+4)² (C) 14) (s²+4)² -8 (s²+4)2 (E) (s²+4)²

A:

Q: Find (e3x + 5sinx)dx. -e3x +5cosx +C O a. 3 e3x+1 -5cosx + C b. 3x + 1 e3x -5 cosx + C OC. -e3x -…

A:

Q: | w(w? + 1)3dw -1 dx х2 sin30cose d0

A: We will answer the first question since exact one wasn't specified, Please resubmit the question and…

Q: E.X; Let T = {E₁ = (-∞,a): a = R}U{R,Ø} be a topology on R and let A = [2,3), B=(3,4), C = (1,5], D…

A: It is given that,  T = Ea=-∞, a : a∈ℝ∪ℝ, ∅ is a topology on ℝ. We have to find the closure of the…

Q: C: Proof that ( a) L (cos²t - sin²t) S s² + 36

A:

Q: Solve S(cosa{x – +)<(1 + +) dx -

A:

Q: One approach to evaluating 2 cos (2x)dx is to first rewrite it as cos(4x) + 1 dx а. cos(2x) – 1 dx…

A: This is the question of integration.

Q: f(x) A B = arcsin x, then lim 1/1/12 0 ㅠ 6 f(x)−ƒ( ² ) X→ X- 1|2 is

A:

Q: L(t cos 2t] s2+2 (s2 +4) 8-4 (s²+4)? s2-2 (s2+4) s2 -4 (s2+4)"

A:

Q: dx 2.

A: In this question we have to solve Integration.

Q: Use the formula £{t^f(t)} (s) = (-1)^(((s)) to help determine the following the expressions. (a) L(t…

A: Solution:-

Q: Find the effect of each of the following operators on the corresponding function. Â = d2 A) f(x) =…

A: In #C d²/dy² , Perheps it will be d²/dx²

Q: (c) Find the value of √a²-x² Sa giving your answer in terms of a. 1+ 2(x + y) x² + y² dx dy,

A:

Q: 3sec2(t) Find f dt ? 6+3 tan (t)

A: Assume (6 + 3*tan(t)) = u and solve the integral.

Q: Find L L e2a sin (3t – 3a) da 3 A) F(s) (s-2)(s² +9) -3 B) F(s) (s+2)(s2 -9) 3s C) F(s) (s-2)(s2 +9)…

A: We find Laplace transform of given function

Q: L{tcost + sint} 3. 2s a. (s²+1) 2s b. (s²+1)² 2s² C. (s²+1)² 2s² d. (s²+1)

A: