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Integrate $x\cos\left(x\right)$ from $\frac{\pi }{6}$ to $\frac{\pi }{2}$

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Basic Derivatives

· Derivative of the linear function

The derivative of the linear function is equal to $1$

$\frac{d}{dx}\left(x\right)=1$

Trigonometric integrals

Apply the integral of the cosine function

$\int\cos\left(x\right)dx=\sin\left(x\right)+C$

Apply the integral of the sine function

$\int\sin\left(x\right)dx=-\cos\left(x\right)+C$
$\int_{\frac{\pi }{6}}^{\frac{\pi }{2}} x\cdot\cos\left(x\right)dx$

Main topic:

Definite integrals

Related formulas:

3. See formulas

Time to solve it:

~ 0.04 seconds