Page 236 - Engineering Mathematics Workbook_Final

Laplace Transforms

5 i t
37. The Laplace transform of e where 41. Evaluate 0   sint dt
i = − 1 is t

s − 5i s + 5i 
(a) (b) (a)  (b)
s − 25 s + 25 2
2
2
s + 5i s − 5i  
(c) (d) (c) (d)
s − 25 s + 25 4 8
2
2
[GATE 2015 – ME-SET 2] [GATE-2007]

38. F(S) is the Laplace transform of the 42. The value of the integral
f t =
t −
2
function ( ) 2t e  sin2 t  
2  −       dt is equal to
F(1) is _______ (correct to two  t  
decimal places). (a) 0 (b) 0.5

[GATE 2018 (ME-MORNING (c) 1 (d) 2
SESSION)] [GATE-2016 (EE-SET 2)]

APPLICATION OF LAPLACE INVERSE LAPLACE TRANSFORM
TRANSFORM IN REAL INTEGRALS  

39. The value of the integral 43. L  − 1 1   =
  (s + 1 )(s − ) 2  
(4 t 
 − 12cos (2 t  ) sin 4 t  ) dt is ____ e 2t e t −


(a)
3 (b) 3
[2015 EC-SET 2] e − e t − e + e t −
2t
2t
(c) (d)
t −

40. The value of  e sint dt = 3 3
0 t
44. The inverse Laplace transform of
 
(a) (b) s + 9
4 2 s + 2 6s + 13 is

(c) (d) 0
3 (a) cos2t + 9sin2t

(b) e − 3t cos2t − 3e − 3t sin2t

(c) e − 3t sin2t + 3e − 3t cos2t

(d) e − 3t cos2t + 3e − 3t sin2t

[GATE-1995]

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