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

= 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

\frac{d}{d x} (\frac{1}{in ( x - 1 )})

\int_{0}^{1} \frac{53}{x ^{5}} d x

\frac{\partial}{\partial x} (- \frac{x}{y})

\int_{- 1}^{1} (2 x - 1)^{2} d x

\frac{d y}{d x} = - 5 - 5 x + y

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