P.o.t.W. #17
■ No GDC ■ for HL students (a) Using the substitution \(x = \sin {\textrm{\theta }} , show that \(\displaystyle\int {\sqrt {1 - {x^2}} } \,{\textrm{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...