nice-calculus-calculate-L-e-t-t-transform-Laplace-

Question Number 130198 by mnjuly1970 last updated on 23/Jan/21

\dots . n i c e c a l c u l u s \dots

c a l c u l a t e ::

L [e^{- t} . \sqrt{t}] \underset{t r a n s f o r m}{\overset{L a p l a c e}{=}} ? \dots

Answered by Dwaipayan Shikari last updated on 23/Jan/21

\int_{0}^{\infty} e^{- (s + 1) t} \sqrt{t} d t

= \frac{1}{{(s + 1)}^{\frac{3}{2}}} Γ (\frac{3}{2}) = \sqrt{\frac{π}{4 {(s + 1)}^{3}}}

Commented by mnjuly1970 last updated on 23/Jan/21

t h a n k s a l o t . .