What is the integral from 0 to pi/2 of e^tcos(3t) ?

The integral from 0 to pi/2 of e^tcos(3t) is (-3e^{pi/2}-1)/(10)

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integral from 0 to pi/2 of e^tcos(3t)

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

\frac{- 3 e ^{\frac{π}{2}} - 1}{10}

Decimal

- 1.54314 \dots

Solution steps

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

Compute the indefinite integral:

\int e^{t} cos (3 t) d t = \frac{3 e ^{t} sin ( 3 t )}{10} + \frac{e ^{t} cos ( 3 t )}{10} + C

Compute the boundaries:

\int_{0}^{\frac{π}{2}} e^{t} cos (3 t) d t = - \frac{3 e ^{\frac{π}{2}}}{10} - \frac{1}{10}

= - \frac{3 e ^{\frac{π}{2}}}{10} - \frac{1}{10}

Simplify

= \frac{- 3 e ^{\frac{π}{2}} - 1}{10}

What is the integral from 0 to pi/2 of e^tcos(3t) ?
The integral from 0 to pi/2 of e^tcos(3t) is (-3e^{pi/2}-1)/(10)