I need to calculate the volume of a body formed by rotating a figure bounded by curves $y=0$, $x=\sqrt{1-y^2}$ and $y=\sqrt{\frac32}x$ around the $Ox$ axis.
The graph of the function and the required volume:
I built a graph and I know the formula, but I can’t figure out which limits to take and what volume to take and subtract from the other in order to get the right answer.
Since you're only working with area above the $x$ axis I'd change the function to $y = \sqrt{1 - x^2}$. Then find what $x$ value the functions intersect at, integrate $\sqrt{1 -x^2} - 1.5x$ from $0$ to that number and apply it to the disk method formula, then just integrate $\sqrt{1 - x^2}$ from that number to $1$ and apply it to the disk method formula.