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

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

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integral from 0 to pi of-xcos(x)

\int_{0}^{π} - x cos (x) d x

2

Solution steps

\int_{0}^{π} - x cos (x) d x

Take the constant out:

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

= - \int_{0}^{π} x cos (x) d x

Apply Integration By Parts

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

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

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

= - [x sin (x) - (- cos (x))]_{0}^{π}

Simplify

= - [x sin (x) + cos (x)]_{0}^{π}

Compute the boundaries:

- 2

= - (- 2)

Simplify

= 2

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

\int_{1}^{x} 1 + t d t

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

\int_{0}^{5} 7 d x

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

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