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}

= [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

\int_{- 2}^{1} (3 + y^{2}) - (2 - y^{2}) d y

\int_{0}^{\frac{π}{6}} sec (x) tan (x) d x

\int_{- 2}^{1} ∣ x + 1 ∣ d x

\int_{2}^{\infty} \frac{4}{x ^{2}} d x

\int_{2}^{4} arcsec (θ) d θ

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