I was trying to find the Volume of a Torus and after sketching it out in Desmos, I thought I found a solution but it doesn't work (or at least when I evaluated it it didn't work).
$V = 2π\int_{-r}^r(\sqrt{r^2-x^2}+R)^2-R^2\ dx$
My reasoning was that I would take the integral of the top half of the circle subtracted by the integral of the line cutting the circle in half and then multiply the whole thing by two to get the total volume. Any help would be appreciated, thanks!