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# Integrate xcos(x) from pi/6 to pi/2

### Formulas

$\frac{3}{\sqrt[3]{3}}$

## Step-by-step explanation

Problem

$\int_{\frac{\pi }{6}}^{\frac{\pi }{2}} x\cdot\cos\left(x\right)dx$
1

Use the integration by parts theorem to calculate the integral $\int x\cos\left(x\right)dx$, using the following formula

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

$\frac{3}{\sqrt[3]{3}}$
$\int_{\frac{\pi }{6}}^{\frac{\pi }{2}} x\cdot\cos\left(x\right)dx$

### Main topic:

Integration by parts

0.32 seconds