What is the integral from 0 to pi of xsin(x) ?

The integral from 0 to pi of xsin(x) is pi

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integral from 0 to pi of xsin(x)

\int_{0}^{π} x sin (x) d x

π

Decimal

3.14159 \dots

Solution steps

\int_{0}^{π} x sin (x) d x

Apply Integration By Parts

: [- x cos (x) - \int - cos (x) d x]_{0}^{π}

= [- x cos (x) - \int - cos (x) d x]_{0}^{π}

\int - cos (x) d x = - sin (x)

= [- x cos (x) - (- sin (x))]_{0}^{π}

Simplify

= [- x cos (x) + sin (x)]_{0}^{π}

Compute the boundaries:

π

= π

\int_{\frac{1}{e}}^{e} ∣ ln (x) ∣ d x

\int_{1}^{4} \frac{1}{1 + x} d x

\int_{1}^{e} sin (ln (x)) d x

\int_{0}^{2} 2 - x^{2} d x

\int_{0}^{4} \frac{1}{1 + x} d x

What is the integral from 0 to pi of xsin(x) ?
The integral from 0 to pi of xsin(x) is pi