What is the integral from 0 to pi/2 of e^{-8x}cos(x) ?

The integral from 0 to pi/2 of e^{-8x}cos(x) is 1/(65e^{4pi)}+8/65

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integral from 0 to pi/2 of e^{-8x}cos(x)

\int_{0}^{\frac{π}{2}} e^{- 8 x} cos (x) d x

\frac{1}{65 e ^{4 π}} + \frac{8}{65}

Solution steps

\int_{0}^{\frac{π}{2}} e^{- 8 x} cos (x) d x

Compute the indefinite integral:

\int e^{- 8 x} cos (x) d x = \frac{e ^{- 8 x} sin ( x )}{65} - \frac{8 e ^{- 8 x} cos ( x )}{65} + C

Compute the boundaries:

\int_{0}^{\frac{π}{2}} e^{- 8 x} cos (x) d x = \frac{1}{65 e ^{4 π}} - (- \frac{8}{65})

= \frac{1}{65 e ^{4 π}} - (- \frac{8}{65})

Simplify

= \frac{1}{65 e ^{4 π}} + \frac{8}{65}

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What is the integral from 0 to pi/2 of e^{-8x}cos(x) ?
The integral from 0 to pi/2 of e^{-8x}cos(x) is 1/(65e^{4pi)}+8/65