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 \cdot 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

n = 1 \sum \infty 3^{- 2 - 2 n} \cdot 2^{3 n + 1}

\frac{\partial}{\partial x} (\frac{x}{2 2})

\int 3 - 2 x x^{2} d x

x = 7 y^{2}, x = 5 + 2 y^{2}

f (x) = 4 x, at x = 25

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