What is the integral from 2pi to 3pi of xsin(x) ?

The integral from 2pi to 3pi of xsin(x) is 5pi

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integral from 2pi to 3pi of xsin(x)

\int_{2 π}^{3 π} x sin (x) d x

5 π

Decimal

15.70796 \dots

Solution steps

\int_{2 π}^{3 π} x sin (x) d x

Apply Integration By Parts

: [- x cos (x) - \int - cos (x) d x]_{2 π}^{3 π}

= [- x cos (x) - \int - cos (x) d x]_{2 π}^{3 π}

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

= [- x cos (x) - (- sin (x))]_{2 π}^{3 π}

Simplify

= [- x cos (x) + sin (x)]_{2 π}^{3 π}

Compute the boundaries:

5 π

= 5 π

\int_{1}^{0} (e^{x} + e^{- 3}) d x

\int_{0}^{r^{2}} r sin (θ) d z

\int_{\frac{π}{2}}^{π} (x sin (x)) d x

\int_{- 1}^{0} - x^{2} - x d x

\int_{2}^{4} x e^{- \frac{x}{2}} d x

What is the integral from 2pi to 3pi of xsin(x) ?
The integral from 2pi to 3pi of xsin(x) is 5pi