1309. Calculate the volume of the body obtained by rotating around the $O y$ axis the curvilinear trapezoid bounded by the hyperbola $x y=4$, the lines $y=1, y=2$ and the $O y$ axis.
Solution. We apply formula (2). From the equation of the curve, we find $x=\frac{4}{y}$, and the limits of integration are given by the condition: $c=1, d=2$. Therefore,

$$
\begin{gathered}
\mathrm{V}=\pi \int_{c}^{d} x^{2} d y=\pi \int_{1}^{2} \frac{16}{y^{2}} d y=\left.\pi\left(-\frac{16}{y}\right)\right|_{1} ^{2}= \\
=16 \pi \left.\frac{1}{y}\right|_{2} ^{1}=16 \pi\left(1-\frac{1}{2}\right)=8 \pi .
\end{gathered}
$$

Calculate the volume of the solid formed by the rotation of the figure bounded by the lines.