What is the integral from 0 to pi of 5xcos(x) ?

The integral from 0 to pi of 5xcos(x) is -10

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integral from 0 to pi of 5xcos(x)

\int_{0}^{π} 5 x cos (x) d x

- 10

Solution steps

\int_{0}^{π} 5 x cos (x) d x

Take the constant out:

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

= 5 \cdot \int_{0}^{π} x cos (x) d x

Apply Integration By Parts

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

= 5 [x sin (x) - \int sin (x) d x]_{0}^{π}

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

= 5 [x sin (x) - (- cos (x))]_{0}^{π}

Simplify

= 5 [x sin (x) + cos (x)]_{0}^{π}

Compute the boundaries:

- 2

= 5 (- 2)

Simplify

= - 10

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\int_{0}^{1} - 2 y + 1 d y

\int_{5}^{6} x d x

\int_{0}^{\frac{π}{4}} t^{2} sin (2 t) d t

What is the integral from 0 to pi of 5xcos(x) ?
The integral from 0 to pi of 5xcos(x) is -10