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

The integral from 0 to pi of 2xcos(x) is -4

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integral from 0 to pi of 2xcos(x)

\int_{0}^{π} 2 x cos (x) d x

- 4

Solution steps

\int_{0}^{π} 2 x cos (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{0}^{π} x cos (x) d x

Apply Integration By Parts

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

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

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

= 2 [x sin (x) - (- cos (x))]_{0}^{π}

Simplify

= 2 [x sin (x) + cos (x)]_{0}^{π}

Compute the boundaries:

- 2

= 2 (- 2)

Simplify

= - 4

\int_{0}^{4} x sin (x) d x

\int_{0}^{3} 5 (1 - e^{y}) d y

\int_{\frac{π}{3}}^{π} cos (x + \frac{π}{3}) d x

\int_{0}^{1} 17 x^{3} 1 - x^{2} d x

\int_{0}^{1} \frac{2 x + 1}{( x + 1 ) ^{2}} d x

What is the integral from 0 to pi of 2xcos(x) ?
The integral from 0 to pi of 2xcos(x) is -4