What is the integral from 0 to pi/4 of e^xsin(x) ?

The integral from 0 to pi/4 of e^xsin(x) is 1/2

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integral from 0 to pi/4 of e^xsin(x)

\int_{0}^{\frac{π}{4}} e^{x} sin (x) d x

\frac{1}{2}

Solution steps

\int_{0}^{\frac{π}{4}} e^{x} sin (x) d x

Compute the indefinite integral:

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

Compute the boundaries:

\int_{0}^{\frac{π}{4}} e^{x} sin (x) d x = 0 - (- \frac{1}{2})

= 0 - (- \frac{1}{2})

Simplify

= \frac{1}{2}

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What is the integral from 0 to pi/4 of e^xsin(x) ?
The integral from 0 to pi/4 of e^xsin(x) is 1/2