F(s) is the Laplace transform of the function f(t) = 2t²e ^-t F (1) is ________ (correct to two decimal places). - General SHORT_ANSWER PYQs Based Test - 13 : Laplace Transforms | ExamTest.live

mediumSHORT_ANSWERPYQs Based Test - 13 : Laplace TransformsGeneral

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F(s) is the Laplace transform of the function f(t) = 2t²e^{- t} F (1) is ________ (correct to two decimal places).

Correct Answer

Solution & Step-by-step Explanation

In the range: 0.48 - 0.52 Concept: L (t^{n}) = \frac{n !}{s ^{n + 1}} L (e^{a t}) = \frac{1}{s - a} L (t^{n} e^{a t}) = \frac{n !}{( s - a ) ^{n + 1}} Calculation: f(t) = 2t²e^{- t} F (s) = L (f (t)) = 2 L (t^{2} e^{- t}) = 2 \times \frac{2 !}{( s + 1 ) ^{2 + 1}} = \frac{4}{( s + 1 ) ^{3}} F (1) = \frac{4}{( 1 + 1 ) ^{3}} = \frac{1}{2} = 0.5

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F(s) is the Laplace transform of the function f(t) = 2t²e^{- t} F (1) is ________ (correct to two decimal places).