What is the integral from 0 to 2pi of xsin(x) ?

The integral from 0 to 2pi of xsin(x) is -2pi

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integral from 0 to 2pi of xsin(x)

\int_{0}^{2 π} x sin (x) d x

- 2 π

Decimal Notation

- 6.28318 \dots

Solution steps

\int_{0}^{2 π} x sin (x) d x

Apply Integration By Parts

: [- x cos (x) - \int - cos (x) d x]_{0}^{2 π}

= [- x cos (x) - \int - cos (x) d x]_{0}^{2 π}

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

= [- x cos (x) - (- sin (x))]_{0}^{2 π}

Simplify

= [- x cos (x) + sin (x)]_{0}^{2 π}

Compute the boundaries:

- 2 π

= - 2 π

\int - 7 x d x

x \to - 2 + lim (\frac{x + 2}{x ^{3} + 8})

\frac{1}{x - 9}

\frac{\partial}{\partial y} (x^{5} + x y^{7} + 4)

y^{^{'}} = \frac{( 3 y ^{2} - x ^{2} )}{2 x y}

What is the integral from 0 to 2pi of xsin(x) ?
The integral from 0 to 2pi of xsin(x) is -2pi