What is the integral from 0 to pi/2 of e^{-7x}cos(x) ?

The integral from 0 to pi/2 of e^{-7x}cos(x) is 1/(50e^{\frac{7pi){2}}}+7/50

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integral from 0 to pi/2 of e^{-7x}cos(x)

\int_{0}^{\frac{π}{2}} e^{- 7 x} cos (x) d x

\frac{1}{50 e ^{\frac{7 π}{2}}} + \frac{7}{50}

Solution steps

\int_{0}^{\frac{π}{2}} e^{- 7 x} cos (x) d x

Compute the indefinite integral:

\int e^{- 7 x} cos (x) d x = \frac{e ^{- 7 x} sin ( x )}{50} - \frac{7 e ^{- 7 x} cos ( x )}{50} + C

Compute the boundaries:

\int_{0}^{\frac{π}{2}} e^{- 7 x} cos (x) d x = \frac{1}{50 e ^{\frac{7 π}{2}}} - (- \frac{7}{50})

= \frac{1}{50 e ^{\frac{7 π}{2}}} - (- \frac{7}{50})

Simplify

= \frac{1}{50 e ^{\frac{7 π}{2}}} + \frac{7}{50}

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What is the integral from 0 to pi/2 of e^{-7x}cos(x) ?
The integral from 0 to pi/2 of e^{-7x}cos(x) is 1/(50e^{\frac{7pi){2}}}+7/50