What is the integral from 0 to pi of e^{3x}*sin(x) ?

The integral from 0 to pi of e^{3x}*sin(x) is (e^{3pi}+1)/(10)

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integral from 0 to pi of e^{3x}*sin(x)

\int_{0}^{π} e^{3 x} \cdot sin (x) d x

\frac{e ^{3 π} + 1}{10}

Decimal Notation

1239.26478 \dots

Solution steps

\int_{0}^{π} e^{3 x} sin (x) d x

Compute the indefinite integral:

\int e^{3 x} sin (x) d x = - \frac{e ^{3 x} cos ( x )}{10} + \frac{3 e ^{3 x} sin ( x )}{10} + C

Compute the boundaries:

\int_{0}^{π} e^{3 x} sin (x) d x = \frac{e ^{3 π}}{10} - (- \frac{1}{10})

= \frac{e ^{3 π}}{10} - (- \frac{1}{10})

Simplify

= \frac{e ^{3 π} + 1}{10}

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What is the integral from 0 to pi of e^{3x}*sin(x) ?
The integral from 0 to pi of e^{3x}*sin(x) is (e^{3pi}+1)/(10)