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

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

(e^{\frac{- x ^{2}}{2}})^{^{'}}

\int \frac{3}{1 - x} d x

\frac{d}{d x} (x^{2} - 4 x + 3)

f (x) = \frac{( e ^{x} )}{x ^{2} + 1}

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