integral sqrt(25 - x^2) dx.

Change the variable, put x=5sin(u), then the integral becomes:

integral 5 sqrt(1-sin^2(u)) 5 cos(u) du = integral 25 cos^2(u) du.

Now use the identity cos^2(u) =(1/2) (1+cos(2u)) so now the integral becomes:

integral 12.5 (1+cos(2u)) du = 12.5 [u + (1/2) sin(2u)]

...........................= 12.5 arcsin(x/5) + 12.5 sin(u)cos(u)

...........................= 12.5 arcsin(x/5) + 12.5 (x/5)sqrt(1-(x/5)^2)

RonL