What is the integral from 0 to pi/3 of e^{-t}cos(t) ?

The integral from 0 to pi/3 of e^{-t}cos(t) is (sqrt(3)-1)/(4e^{pi/3)}+1/2

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integral from 0 to pi/3 of e^{-t}cos(t)

\int_{0}^{\frac{π}{3}} e^{- t} cos (t) d t

\frac{3 - 1}{4 e ^{\frac{π}{3}}} + \frac{1}{2}

Solution steps

\int_{0}^{\frac{π}{3}} e^{- t} cos (t) d t

Compute the indefinite integral:

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

Compute the boundaries:

\int_{0}^{\frac{π}{3}} e^{- t} cos (t) d t = \frac{3 - 1}{4 e ^{\frac{π}{3}}} - (- \frac{1}{2})

= \frac{3 - 1}{4 e ^{\frac{π}{3}}} - (- \frac{1}{2})

Simplify

= \frac{3 - 1}{4 e ^{\frac{π}{3}}} + \frac{1}{2}

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What is the integral from 0 to pi/3 of e^{-t}cos(t) ?
The integral from 0 to pi/3 of e^{-t}cos(t) is (sqrt(3)-1)/(4e^{pi/3)}+1/2