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

The integral from 0 to 2pi of cos(3t)e^{-2t} is -2/(13e^{4pi)}+2/13

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to 2pi of cos(3t)e^{-2t}

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

- \frac{2}{13 e ^{4 π}} + \frac{2}{13}

Decimal

0.15384 \dots

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

\int_{0}^{2 π} cos (3 t) e^{- 2 t} d t = - \frac{2}{13 e ^{4 π}} - (- \frac{2}{13})

= - \frac{2}{13 e ^{4 π}} - (- \frac{2}{13})

Simplify

= - \frac{2}{13 e ^{4 π}} + \frac{2}{13}

What is the integral from 0 to 2pi of cos(3t)e^{-2t} ?
The integral from 0 to 2pi of cos(3t)e^{-2t} is -2/(13e^{4pi)}+2/13