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

The integral from 0 to pi/2 of e^{2x}sin(x) is (2e^pi+1)/5

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

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

\frac{2 e ^{π} + 1}{5}

Decimal

9.45627 \dots

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

\int_{0}^{\frac{π}{2}} e^{2 x} sin (x) d x = \frac{2 e ^{π}}{5} - (- \frac{1}{5})

= \frac{2 e ^{π}}{5} - (- \frac{1}{5})

Simplify

= \frac{2 e ^{π} + 1}{5}

What is the integral from 0 to pi/2 of e^{2x}sin(x) ?
The integral from 0 to pi/2 of e^{2x}sin(x) is (2e^pi+1)/5