Question: Let f(t)be a function defined for all positive values oft. The Laplace Transform off(t)is defined by the following if the improper integral exists.F(s)=0e-stf(t)dtLaplace Transforms are

Let f(t)be a function defined for all positive values oft. The Laplace Transform off(t)is defined by the following if the improper integral exists.F(s)=0e-stf(t)dtLaplace Transforms are used to solve differential equations. Find the Laplace Transform of the function.f(x)=2Part 1of3Note that the Laplace transform is defined asF(s)=0e-stf(t)dtIn order to find the Laplace transform off(t)=2, substitute this value in the above integral.F(s)=0e-st(2,2)dtThis isan improper integral as the upper limitis. Therefore apply the definition of improper integral by taking limitasb.F(s)=limb0b2e-stdtPart 2of3Take the antiderivative of2e-st which isF(s)=limb[2e-st-s]0b=limb2-s[e-bt-e0]=limb2-s[e-bt]-2-s(1)=2-s(0)+2s=2s,(s>0)

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