I am having a bit of a hard time figuring this one out. Would be very nice if anyone would like to help me (no more forehead banging against wall :))
while: $ 0 \leq x \leq L$
The function is: $\xi(x) = k\sqrt{x(L-x)} $ & $\xi(x)dx = k\sqrt{x(L-x)}dx $
$m = \int_{0}^{L}k\sqrt{x(L-x)}dx = k\int_{0}^{L}\sqrt{Lx-x^2}dx = k\int_{0}^{L}\sqrt{\frac{L^2}{4}-(x-\frac{L}{2})^2}dx$
I cannot understand how they develop that last step. Any help is much appreciated!
Thank you!