Level:
Project ID:
9000100003
Accepted:
1
Clonable:
0
Easy:
0
The function \(f(x) = x^{2} + 2\)
is graphed in the picture. Consider the region between the graph of the function on the interval
\([ 0;\, 1] \), both axes
and the line \(x = 1\).
Find the formula for the volume of the solid of revolution obtained by revolving this region
about \(y\)-axis.
\(V =\pi \int _{ 0}^{3}1\, \mathrm{d}y -\pi \int _{2}^{3}(\sqrt{y - 2})^{2}\, \mathrm{d}y\)
\(V =\pi \int _{ 0}^{3}(\sqrt{y - 2})^{2}\, \mathrm{d}y\)
\(V =\pi \int _{ 2}^{3}(\sqrt{y - 2})^{2}\, \mathrm{d}y -\pi \int _{0}^{3}1\, \mathrm{d}y\)
\(V =\pi \int _{ 2}^{3}(\sqrt{y - 2})^{2}\, \mathrm{d}y\)