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_{0}^{2} 3 e^{x^{2} - x} d x

\int_{0}^{3} (x - 4)^{3} d x

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

\int_{0}^{π} (sin (θ))^{2} d θ

\int_{2}^{5} (6 x^{2} - 3 x + 5) d x

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