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## Homework Statement

Find the area between the curve [tex]y=e^{-x}\left|sinx\right|[/tex] and the straight line y=0 for [tex]x\geq 0[/tex]

## The Attempt at a Solution

[tex]\int_{0}^{\infty}e^{-x}\left|sinx\right|dx=-e^{-x}\left|sinx\right|+\int_{0}^{\infty}e^{-x}\left|cosx\right|dx[/tex]

[tex]=-e^{-x}\left|sinx\right|-e^{-x}\left|cosx\right|-\int_{0}^{\infty}e^{-x}\left|sinx\right|dx[/tex]

[tex]\int_{0}^{\infty}e^{-x}\left|sinx\right|dx=\frac{-e^{-x}\left|sinx\right|-e^{-x}\left|cosx\right|}{2}[/tex]