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

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

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integral from pi to 2pi of xcos(x)

\int_{π}^{2 π} x cos (x) d x

2

Solution steps

\int_{π}^{2 π} x cos (x) d x

Apply Integration By Parts

: [x sin (x) - \int sin (x) d x]_{π}^{2 π}

= [x sin (x) - \int sin (x) d x]_{π}^{2 π}

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

= [x sin (x) - (- cos (x))]_{π}^{2 π}

Simplify

= [x sin (x) + cos (x)]_{π}^{2 π}

Compute the boundaries:

2

= 2

\int_{0}^{16} f (t) d t

\int_{0}^{2} \frac{32}{x ^{2} + 4} d x

\int_{1}^{2} x^{2} + 3 d x

\int_{- π}^{π} cos (m x) d x

\int_{1}^{3} \frac{y}{( y + 1 ) ( y ^{2} + 2 )} d y

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