What is the integral from 0 to pi/2 of e^{-6x}cos(x) ?

The integral from 0 to pi/2 of e^{-6x}cos(x) is 1/(37e^{3pi)}+6/37

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integral from 0 to pi/2 of e^{-6x}cos(x)

\int_{0}^{\frac{π}{2}} e^{- 6 x} cos (x) d x

\frac{1}{37 e ^{3 π}} + \frac{6}{37}

Decimal

0.16216 \dots

Solution steps

\int_{0}^{\frac{π}{2}} e^{- 6 x} cos (x) d x

Compute the indefinite integral:

\int e^{- 6 x} cos (x) d x = \frac{e ^{- 6 x} sin ( x )}{37} - \frac{6 e ^{- 6 x} cos ( x )}{37} + C

Compute the boundaries:

\int_{0}^{\frac{π}{2}} e^{- 6 x} cos (x) d x = \frac{1}{37 e ^{3 π}} - (- \frac{6}{37})

= \frac{1}{37 e ^{3 π}} - (- \frac{6}{37})

Simplify

= \frac{1}{37 e ^{3 π}} + \frac{6}{37}

What is the integral from 0 to pi/2 of e^{-6x}cos(x) ?
The integral from 0 to pi/2 of e^{-6x}cos(x) is 1/(37e^{3pi)}+6/37