Find: Using complex integration, prove the inverse Laplace transform of F(s) is sin(2t) L-¹ [F(s)] = 1

Q: 5. Find the value of the integral using Laplace Transform (a) je ¹ sin2tdt 0 (b) je' costat

A:

Q: Let a= (123)(145) in S6. Write a102 in disjoint cycle form. O (32541) O (16)(24) O None of these…

A:

Q: Use integration by parts to find the Laplace transform. f(t) =t coshat

A: To Find: The laplace transform of ft=tcoshat

Q: Find the Laplace transform of: (a) cosh at (b) sinh at

A: Given (a)cosh at  and (b)sinh at We have to find the Laplace transform of them…

Q: sin mt dt 2 b) By using the Laplace transform show that L

A:

Q: cos x, 0 a

A:

Q: Apply the theorem of integration of transforms to find the Laplace transform of f(t)=2sin5t. Show…

A:

Q: Construct the truth table of the given compound statement (~b^a)→(avb)

A: The given compound statement is: ~b∧a→a∨b

Q: cos x, 0a

A:

Q: Find the Laplace transform of f (t) = t using direct integration. Find the Laplace transform of the…

A: We have to find the Laplace transformation of the functions (a) ft=t2 and (b) ft=sin2t using direct…

Q: (ii): f(t) = sin (t + 7)+ e³' cosh 5t

A:

Q: Evaluate using Laplace Transform: 00 2 sin f (t) = dt et

A:

Q: Find the Laplace transform of sin t cos t

A: Given f(t) = sin t cos t = 2sintcost2 = sin(2t)2

Q: | (t – cos(3t))e-'dt

A: Using definition of Laplace transform.

Q: S(1) = >1

A:

Q: ii) using the Fourier Transforms, Calculate dx.

A:

Q: Using the properties of laplace transform, find [sin t sin h t cos t cosh t)

A: We have to find the Laplace transform.

Q: Find the Laplace transform using convolution theorem: Te2" sin(2(t - T))dr.

A: So, here f(t) = sin(2t) and g(t) = t e2t.

Q: tsin 3t fre>=5. ー3七

A:

Q: Derive the laplace transform for f(t)= 3 e-St

A:

Q: -4t L {2+ + == ¹²}

A:

Q: f(t) =sin 4x/x. Find the Laplace transform

A:

Q: Using integration, derive the Laplace transform of: L(cosh at)

A: We will use the definition of laplace transform and concept of definite integration to derive the…

Q: b) By applying the definition of Laplace Transform, find the Laplace transform for f(t) = cos 3t.…

A:

Q: f(x) = (sinx if 0 π

A: This is a question of Fourier Analysis.

Q: Apply the definition of the Laplace transform to find sin bt.

A:

Q: If x= 1.3 + 3.6 1.3.5 3.6.9 + 1.3.5.7 3.6.9.12 + then P.T. 9₂²°²+24x=11 ,

A:

Q: fx, þx| a' Find the Fourier transform ofƒ (x) = %3D

A:

Q: .2 TX e cos(x)

A: Given, fx=e-πx2cosx ∴ℱfx=f~p=12π∫-∞∞eipxfxdx⇒ℱe-πx2cosx=12π∫-∞∞eipxe-πx2cosxdx…

Q: Find the Laplace transform of the function f(t) : For this particular problem, use the integral…

A: