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integral_0^? e^(-a x) sin(b x) dx Solution Integrate by parts Let u = sin(x) =>

ID: 2971626 • Letter: I

Question

integral_0^? e^(-a x) sin(b x) dx

Explanation / Answer

Integrate by parts Let u = sin(x) => u' = cos(x) And v' = e^(-x) => v = -e^(-x) => A = -sin(x)*e^(-x) - ? cos(x)(-e^(-x)) dx = -sin(x)*e^(-x) + ? cos(x)e^(-x) dx Integrate by parts: Let p = cos(x) => p' = -sin(x) And w' = e^(-x) => w = -e^(-x) => A = sin(x)*e^(-x) + [-cos x*e^(-x) - ? sin(x) e^(-x) dx] A = sin(x) e^(-x) - cos(x) e^(-x) - A ....(this is the trick: you should notice that A =? sin(x) e^(-x) dx Take A to the other side 2A = sin(x) e^(-x) - cos(x) e^(-x) => A = [sin(x) e^(-x) - cos(x) e^(-x)] /2

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