Question

Use Theorem 7. 1. 1 to find L{f(t)}\mathscr{L}\{f(t)\}. f(t)=2t4f(t)=2 t^{4}

Solution

Verified
Step 1
1 of 2

Laplace transform of given function by using Theorem 7.2 is

f(t)=2t4f(t)=2t^{4}

According to Theorem 7.2 b

L(tn)=n!sn+1\mathcal{L}(t^{n})=\dfrac{n!}{s^{n+1}}

L(2t4)=24!s5=48s5\mathcal{L}(2t^{4})=2\dfrac{4!}{s^{5}}=\dfrac{48}{s^{5}}

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