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

The integral from 0 to pi/2 of e^{-4x}cos(x) is 1/(17e^{2pi)}+4/17

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integral from 0 to pi/2 of e^{-4x}cos(x)

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

\frac{1}{17 e ^{2 π}} + \frac{4}{17}

Decimal

0.23540 \dots

Solution steps

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

Compute the indefinite integral:

\int e^{- 4 x} cos (x) d x = \frac{e ^{- 4 x} sin ( x )}{17} - \frac{4 e ^{- 4 x} cos ( x )}{17} + C

Compute the boundaries:

\int_{0}^{\frac{π}{2}} e^{- 4 x} cos (x) d x = \frac{1}{17 e ^{2 π}} - (- \frac{4}{17})

= \frac{1}{17 e ^{2 π}} - (- \frac{4}{17})

Simplify

= \frac{1}{17 e ^{2 π}} + \frac{4}{17}

What is the integral from 0 to pi/2 of e^{-4x}cos(x) ?
The integral from 0 to pi/2 of e^{-4x}cos(x) is 1/(17e^{2pi)}+4/17