Explanation

(d)
$\int_{0}^{a}\sqrt{a^{2} - x^{2}}\ dx = \left\lbrack \frac{x}{2}\sqrt{a^{2} - x^{2}} + \frac{a^{2}}{2}\sin^{- 1}\left( \frac{x}{a} \right) \right\rbrack_{0}^{a}$
$= \left\lbrack 0 + \frac{a^{2}}{2}\sin^{- 1}(1) - 0 - \frac{a^{2}}{2}\sin^{- 1}(0) \right\rbrack$
$= \frac{a^{2}}{2}.\frac{\pi}{2} - 0 = \frac{a^{2}\pi}{4}$