Solve V = ∫ (from 0 to 1) of pi(y-arcsiny)^2 wrt y-int_0^1pi(arcsiny)^2dy

$$V = \int _ { 0 } ^ { 1 } \pi ( y - \arcsin y ) ^ { 2 } d y - \int _ { 0 } ^ { 1 } \pi ( \arcsin y ) ^ { 2 } d y$$

Solve for V (complex solution)

$$V=\int _{0}^{1}\pi \left(-\arcsin(y)+y\right)^{2}\mathrm{d}y-\int _{0}^{1}\pi \left(\arcsin(y)\right)^{2}\mathrm{d}y$$

Assign V (complex solution)

$$V≔\int _{0}^{1}\pi \left(-\arcsin(y)+y\right)^{2}\mathrm{d}y-\int _{0}^{1}\pi \left(\arcsin(y)\right)^{2}\mathrm{d}y$$

Solve for V

$$V=\int _{0}^{1}\pi \left(-\arcsin(y)+y\right)^{2}\mathrm{d}y-\int _{0}^{1}\pi \left(\arcsin(y)\right)^{2}\mathrm{d}y$$

$$|y|\leq 1$$

Assign V

$$V≔\int _{0}^{1}\pi \left(-\arcsin(y)+y\right)^{2}\mathrm{d}y-\int _{0}^{1}\pi \left(\arcsin(y)\right)^{2}\mathrm{d}y$$

$$|y|\leq 1$$