HL only■ No GDC ■(a) Using the substitution \(x = \sin {\rm{\theta }}\), show that \(\displaystyle\int {\sqrt {1 - {x^2}} } \,{\rm{d}}x = \frac{{\arcsin x + x\sqrt {1 - {x^2}} }}{2}\).(b) Torus is the mathematical name for a donut which is a nice example of a solid of revolution because a donut can be formed by rotating a circle \(360^\circ \) about a line.Using the result from (a), find the exact volume of the donut that is formed by rotating the circle with center at \(\left( {0,2} \right)\) and radius of 1 unit about the x-axis.