Chapter 11.12, Problem 12P

In Problems 4 to 13, identify each of the integrals as an elliptic integral (see Examples 1 and 2 ). Learn the notation of your computer program (see Problem 3 ) and then evaluate the integral by computer.

${\displaystyle {\int }_0^{1/2}\frac{\sqrt{100-t^2}}{\sqrt{1-t^2}}}dt$