What is the integral from 0 to 1 of e^{-2x}cos(3x) ?

The integral from 0 to 1 of e^{-2x}cos(3x) is (3sin(3)-2cos(3))/(13e^2)+2/13

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integral from 0 to 1 of e^{-2x}cos(3x)

\int_{0}^{1} e^{- 2 x} cos (3 x) d x

\frac{3 sin ( 3 ) - 2 cos ( 3 )}{13 e ^{2}} + \frac{2}{13}

Decimal Notation

0.17886 \dots

Solution steps

\int_{0}^{1} e^{- 2 x} cos (3 x) d x

Compute the indefinite integral:

\int e^{- 2 x} cos (3 x) d x = \frac{3 e ^{- 2 x} sin ( 3 x )}{13} - \frac{2 e ^{- 2 x} cos ( 3 x )}{13} + C

Compute the boundaries:

\int_{0}^{1} e^{- 2 x} cos (3 x) d x = \frac{3 sin ( 3 ) - 2 cos ( 3 )}{13 e ^{2}} - (- \frac{2}{13})

= \frac{3 sin ( 3 ) - 2 cos ( 3 )}{13 e ^{2}} - (- \frac{2}{13})

Simplify

= \frac{3 sin ( 3 ) - 2 cos ( 3 )}{13 e ^{2}} + \frac{2}{13}

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What is the integral from 0 to 1 of e^{-2x}cos(3x) ?
The integral from 0 to 1 of e^{-2x}cos(3x) is (3sin(3)-2cos(3))/(13e^2)+2/13