Elliptic Integral D
Let $0\leqslant \phi\leqslant\frac{\pi}{2}$ and $-1 \leqslant k\leqslant 1$ with the condition $k^2\sin^2\phi < 1$, this calculator evaluates the incomplete elliptic integral $D(\phi,k)$: \[ D(\phi,k)=\int_0^\phi \frac{\sin^2\theta}{\sqrt{1-k^2\sin^2\theta}}\;d\theta \] and if $-1 < k < 1$, it also evaluates the complete elliptic integral \[ D\left(\frac{\pi}{2},k\right)=\int_0^\frac{\pi}{2} \frac{\sin^2\theta}{\sqrt{1-k^2\sin^2\theta}}\;d\theta \]