Find the volume of the solid formed when the region bounded by the parabola y = x^2 - 2 is rotated about (i) the X-axis (ii) the Y-axis.
How exactly do I do this question? For the previous questions, there was a limit for both x and y but now...
Find the volume of the solid formed when the region bounded by the parabola y = x^2 - 2 is rotated about (i) the X-axis (ii) the Y-axis.
How exactly do I do this question? For the previous questions, there was a limit for both x and y but now...
For the first part since you are rotating around the x-axis you can find theh intercepts by setting y=0
$\displaystyle 0=x^2-2 \iff x=\pm \sqrt{2}$
So your integral becomes
$\displaystyle \int_{-\sqrt{2}}^{\sqrt{2}}\pi (x^2-2)^2dx=2\pi\int_{0}^{\sqrt{2}}(x^2-2)^2dx=...$
Try something similar for the 2nd one.