- #1
vilhelm
- 37
- 0
Problem
The area between [tex]y=x^{-2}[/tex] and x=1 & y=e is rotating around the y-axis. What is the volume?
Attempt
[tex]\pi\left( r_{outer\mbox{}} \right)^{2}\; -\; \pi \left( r_{inner\mbox{}} \right)^{2} \; \; \; \delta y[/tex].
[tex]\frac{1}{x^{2}}=y\; gives\; \frac{1}{y}=x^{2}\; and\; r=\sqrt{y}[/tex]
[tex]V=\pi \int_{1}^{e}{\frac{1}{y}-1\; dy}[/tex]
The area between [tex]y=x^{-2}[/tex] and x=1 & y=e is rotating around the y-axis. What is the volume?
Attempt
[tex]\pi\left( r_{outer\mbox{}} \right)^{2}\; -\; \pi \left( r_{inner\mbox{}} \right)^{2} \; \; \; \delta y[/tex].
[tex]\frac{1}{x^{2}}=y\; gives\; \frac{1}{y}=x^{2}\; and\; r=\sqrt{y}[/tex]
[tex]V=\pi \int_{1}^{e}{\frac{1}{y}-1\; dy}[/tex]