1. ## Volumes

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...

2. Originally Posted by xwrathbringerx
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...
see this pic find where the curve intersect with the x-axis and the y-axis this is the limits you want y change from -2 to 0 and x from $\displaystyle -\sqrt{2}$ to $\displaystyle \sqrt{2}$

3. Originally Posted by xwrathbringerx
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

$\displaystyle 0=x^2-2 \iff x=\pm \sqrt{2}$

$\displaystyle \int_{-\sqrt{2}}^{\sqrt{2}}\pi (x^2-2)^2dx=2\pi\int_{0}^{\sqrt{2}}(x^2-2)^2dx=...$