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

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

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integral from 0 to pi of cos(x)x

\int_{0}^{π} cos (x) x d x

- 2

Solution steps

\int_{0}^{π} cos (x) x d x

Apply Integration By Parts

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

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

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

= [x sin (x) - (- cos (x))]_{0}^{π}

Simplify

= [x sin (x) + cos (x)]_{0}^{π}

Compute the boundaries:

- 2

= - 2

\int_{π}^{0} cos (x) d x

\int_{1}^{8} 4 x^{\frac{1}{3}} d x

\int_{2}^{4} x^{2} - 3 x + 4 d x

\int_{1}^{2} \frac{y ^{2} + 1}{y ^{2}} d y

\int_{0}^{2 π} sin^{7} (x) d x

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