What is the integral from 0 to pi/2 of e^{2x}cos(x) ?

The integral from 0 to pi/2 of e^{2x}cos(x) is (e^pi-2)/5

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integral from 0 to pi/2 of e^{2x}cos(x)

\int_{0}^{\frac{π}{2}} e^{2 x} cos (x) d x

\frac{e ^{π} - 2}{5}

Decimal

4.22813 \dots

Solution steps

\int_{0}^{\frac{π}{2}} e^{2 x} cos (x) d x

Compute the indefinite integral:

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

Compute the boundaries:

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

= \frac{e ^{π}}{5} - \frac{2}{5}

Simplify

= \frac{e ^{π} - 2}{5}

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