Originally Posted by

**Em Yeu Anh** Thank you,

alright I'll try that again:

$\displaystyle \frac{d}{dx}\int_0^{x^2}f(t)dt = -{\pi}xsin{\pi}x + cos{\pi}x $

$\displaystyle f(x^2)*2x = -{\pi}xsin{\pi}x + cos{\pi}x $

$\displaystyle f(x^2) = \frac{-{\pi}sin{\pi}x}{2} + \frac{cos{\pi}x}{2x} $

$\displaystyle f(4) = \frac{1}{4} $

Assuming the same method will be applicable to part 2,

$\displaystyle \frac{d}{d{\color{red}a}}\int_0^af(x)dx = a + \frac{acosa}{2} - \frac{{\pi}sina}{2} $ Mr F says: 1. Note the red a, and 2. Your derivative of the right hand side with respect to a is missing a term.

$\displaystyle f({\pi}/2) = \frac{\pi}{2} + \frac{({\pi}/2)cos({\pi}/2)}{2} - \frac{{\pi}sin({\pi}/2)}{2} $

$\displaystyle f({\pi}/2) = 0 $