Prove that: ∫√a^2 - x^2 dx = x/2√a^2 - x^2 + a^2/2 sin^-1 (x/a) + c

Question

Prove that:

∫ \(\sqrt{{a^2}-{x^2}}\,dx =\frac{x}{2}\sqrt{{a^2}-{x^2}} + \frac{a^2}{2} \,sin^{-1}\,(\frac{x}{a}) + c\)

Answer 1

Let I = ∫ \(\sqrt{{a^2}-{x^2}}.1dx\)

where c = \(\frac{c_1}{2}\)