What is the integral from 0 to 1 of e^{2x}cos(pix) ?

The integral from 0 to 1 of e^{2x}cos(pix) is (-2e^2-2)/(pi^2+4)

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integral from 0 to 1 of e^{2x}cos(pix)

\int_{0}^{1} e^{2 x} cos (π x) d x

\frac{- 2 e ^{2} - 2}{π ^{2} + 4}

Decimal Notation

- 1.20970 \dots

Solution steps

\int_{0}^{1} e^{2 x} cos (π x) d x

Compute the indefinite integral:

\int e^{2 x} cos (π x) d x = \frac{π e ^{2 x} sin ( π x )}{π ^{2} + 4} + \frac{2 e ^{2 x} cos ( π x )}{π ^{2} + 4} + C

Compute the boundaries:

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

= - \frac{2 e ^{2}}{π ^{2} + 4} - \frac{2}{π ^{2} + 4}

Simplify

= \frac{- 2 e ^{2} - 2}{π ^{2} + 4}

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What is the integral from 0 to 1 of e^{2x}cos(pix) ?
The integral from 0 to 1 of e^{2x}cos(pix) is (-2e^2-2)/(pi^2+4)