Question

Value of \(\int_{-\infty}^\infty e^t \,Sin(t) \,dt\) = ?

(a) 0.50

(b) 0.25

(c) 0.17

(d) 0.12

I had been asked this question by my college professor while I was bunking the class.

Enquiry is from Laplace Transform by Properties in division Laplace Transform of Engineering Mathematics

Answer 1

Right choice is (a) 0.50

The explanation: L(Sin(2t)) = \(\int_{-\infty}^\infty e^{-st} \,Sin(t)dt\) = 1/(s^2 + 1)

Putting s = -1

\(\int_{-\infty}^\infty e^t \,Sin(t)dt\) = 0.5.