29.27. Calculate the area under the graph of the function $y=$ $=\sin x$ on the interval from 0 to $\pi$.

## 29.5. Calculation of Volumes

Let a body be located in space with rectangular coordinates $O x y z$, such that the projection of this body onto the $O x$ axis is the segment $[a, b]$. Suppose that a plane passing through
a point $x$ of the segment $[a, b]$ perpendicular to the $O x$ axis cuts out a figure of area $S(x)$ on this body. Then the volume of this body is given by $\int_{a}^{b} S(x) d x$.
29.27. The desired area is equal to $\int_{0}^{\pi} \sin x d x=-\left.\cos x\right|_{0} ^{\pi}=2$.