What is the integral from 0 to pi of e^{-sx}sin(x) ?

The integral from 0 to pi of e^{-sx}sin(x) is (e^{-pis}+1)/(s^2+1)

Popular >

integral from 0 to pi of e^{-sx}sin(x)

\int_{0}^{π} e^{- s x} sin (x) d x

\frac{e ^{- π s} + 1}{s ^{2} + 1}

Solution steps

\int_{0}^{π} e^{- s x} sin (x) d x

Compute the indefinite integral:

\int e^{- s x} sin (x) d x = - \frac{e ^{- s x} cos ( x )}{1 + s ^{2}} - \frac{s e ^{- s x} sin ( x )}{1 + s ^{2}} + C

Compute the boundaries:

\int_{0}^{π} e^{- s x} sin (x) d x = \frac{e ^{- π s}}{s ^{2} + 1} - (- \frac{1}{1 + s ^{2}})

= \frac{e ^{- π s}}{s ^{2} + 1} - (- \frac{1}{1 + s ^{2}})

Simplify

= \frac{e ^{- π s} + 1}{s ^{2} + 1}

\int_{0}^{π} e^{c o s (x)} d x

\int_{0}^{3} 2 x + 3 d x

\int_{\frac{x}{2}}^{1 - \frac{x}{2}} (2 - x - 2 y) d y

\int_{0}^{1} 2 x^{2} + 2 d x

\int_{0}^{\frac{π}{4}} \frac{1}{cos ^{4} ( x )} d x

What is the integral from 0 to pi of e^{-sx}sin(x) ?
The integral from 0 to pi of e^{-sx}sin(x) is (e^{-pis}+1)/(s^2+1)