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

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

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integral from 0 to pi of e^{x/2}cos(x)

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

\frac{- 2 e ^{\frac{π}{2}} - 2}{5}

Decimal

- 2.32419 \dots

Solution steps

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

Compute the indefinite integral:

\int e^{\frac{x}{2}} cos (x) d x = 2 (\frac{2}{5} e^{\frac{x}{2}} sin (x) + \frac{1}{5} e^{\frac{x}{2}} cos (x)) + C

Compute the boundaries:

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

= - 2 \cdot \frac{e ^{\frac{π}{2}}}{5} - \frac{2}{5}

Simplify

= \frac{- 2 e ^{\frac{π}{2}} - 2}{5}

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