$\displaystyle

\int\sqrt{25-t^2}\,dt

$

a = 5 u = t so....

t = 5 sin $\displaystyle \theta$

sqrt(25-(5 sin $\displaystyle \theta$)^2 )

sqrt(25 cos^2 $\displaystyle \theta$)

25 cos $\displaystyle \theta$

25 sin $\displaystyle \theta$

25 sin(t/5) is what I get after substituting in for t. I know this isn't right but could someone explain why?