What is the integral from 0 to 1 of e^{-x}cos(2x) ?

The integral from 0 to 1 of e^{-x}cos(2x) is (2sin(2)-cos(2))/(5e)+1/5

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integral from 0 to 1 of e^{-x}cos(2x)

\int_{0}^{1} e^{- x} cos (2 x) d x

\frac{2 sin ( 2 ) - cos ( 2 )}{5 e} + \frac{1}{5}

Decimal Notation

0.36442 \dots

Solution steps

\int_{0}^{1} e^{- x} cos (2 x) d x

Compute the indefinite integral:

\int e^{- x} cos (2 x) d x = \frac{2 e ^{- x} sin ( 2 x )}{5} - \frac{e ^{- x} cos ( 2 x )}{5} + C

Compute the boundaries:

\int_{0}^{1} e^{- x} cos (2 x) d x = \frac{2 sin ( 2 ) - cos ( 2 )}{5 e} - (- \frac{1}{5})

= \frac{2 sin ( 2 ) - cos ( 2 )}{5 e} - (- \frac{1}{5})

Simplify

= \frac{2 sin ( 2 ) - cos ( 2 )}{5 e} + \frac{1}{5}

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What is the integral from 0 to 1 of e^{-x}cos(2x) ?
The integral from 0 to 1 of e^{-x}cos(2x) is (2sin(2)-cos(2))/(5e)+1/5