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

The integral from 0 to pi of e^xsin(2x) is (-2e^pi+2)/5

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integral from 0 to pi of e^xsin(2x)

\int_{0}^{π} e^{x} sin (2 x) d x

\frac{- 2 e ^{π} + 2}{5}

Decimal Notation

- 8.85627 \dots

Solution steps

\int_{0}^{π} e^{x} sin (2 x) d x

Compute the indefinite integral:

\int e^{x} sin (2 x) d x = - \frac{2 e ^{x} cos ( 2 x )}{5} + \frac{e ^{x} sin ( 2 x )}{5} + C

Compute the boundaries:

\int_{0}^{π} e^{x} sin (2 x) d x = - \frac{2 e ^{π}}{5} - (- \frac{2}{5})

= - \frac{2 e ^{π}}{5} - (- \frac{2}{5})

Simplify

= \frac{- 2 e ^{π} + 2}{5}

\int_{\frac{π}{4}}^{π} sin^{5} (x) d x

\int_{0}^{1} x^{4} - x^{6} d x

\int_{7}^{14} x^{2} - 16 d x

\int_{1}^{10} \frac{x - 1}{x} d x

\int_{0}^{2 π} 5 t \cdot 2 d t

What is the integral from 0 to pi of e^xsin(2x) ?
The integral from 0 to pi of e^xsin(2x) is (-2e^pi+2)/5