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

Popular >

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}

Decimal Notation

0.12307 \dots

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}

\int_{3}^{6} x^{2} + 3 d x

\int_{1}^{6} \frac{x}{x + 3} d x

\int_{0}^{2} sec^{3} (x) d x

\int_{- 4}^{1} (4 - x^{2} - 3 x) d x

\int_{0}^{2.5} 127 \cdot 6.1 d x

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