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 Notation

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_{0}^{1.5} \frac{3}{2 x ^{2}} d x

\int_{0}^{2} (- x^{2} + 4 x - x^{2}) d x

\int_{0}^{1} (2 + x^{3}) d x

\int_{0}^{5} \frac{1}{x ^{2} - 6 x + 9} d x

\int_{0}^{6} x (6 - x) 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