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

The integral from 0 to pi of 4xcos(x) is -8

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integral from 0 to pi of 4xcos(x)

\int_{0}^{π} 4 x cos (x) d x

- 8

Solution steps

\int_{0}^{π} 4 x cos (x) d x

Take the constant out:

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

= 4 \cdot \int_{0}^{π} x cos (x) d x

Apply Integration By Parts

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

= 4 [x sin (x) - \int sin (x) d x]_{0}^{π}

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

= 4 [x sin (x) - (- cos (x))]_{0}^{π}

Simplify

= 4 [x sin (x) + cos (x)]_{0}^{π}

Compute the boundaries:

- 2

= 4 (- 2)

Simplify

= - 8

\int_{\frac{1}{2}}^{1} \frac{1}{x ^{2}} e^{\frac{1}{x}} d x

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\int_{0}^{1} [\frac{5 x - 2}{x ^{2} - 4}] d x

\int_{- 2}^{2} \frac{x ^{2}}{2} - 3 d x

\int_{0}^{1} 1 + 2 x^{2} d x

What is the integral from 0 to pi of 4xcos(x) ?
The integral from 0 to pi of 4xcos(x) is -8