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

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

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integral from 0 to pi of x(sin(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_{1}^{2} \frac{1}{1 - x ^{2}} d x

\int_{1}^{2} \frac{e ^{\frac{1}{x}}}{x ^{3}} d x

\int_{- 2}^{2} (x^{2} - 2) d x

\int_{1}^{2} \frac{x + 3}{x ( x + 2 )} d x

\int_{1}^{5} x^{2} + 2 d x

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