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

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

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integral from 0 to 2pi of xcos(x)

\int_{0}^{2 π} x cos (x) d x

0

Solution steps

\int_{0}^{2 π} x cos (x) d x

Apply Integration By Parts

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

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

= [x sin (x) - (- cos (x))]_{0}^{2 π}

Simplify

= [x sin (x) + cos (x)]_{0}^{2 π}

Compute the boundaries:

0

= 0

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