# Incomplete elliptic integral of the 1st kind F(φ,k) Calculator

## Calculates the incomplete elliptic integral of the first kind F(φ,k).

 $F(\phi,k)={\large\int_{\small 0}^{\hspace{25}\small\phi}\frac{d\theta}{\sqrt{1-k^2sin^2\theta}}$
 φ degree   -360≦φ≦360 radian    -2π≦φ≦2π k -1≦k≦1
 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt
 ・ F(x,k) can be used at x=sin(φ).$\normal Incomplete\ elliptic\ integral\\\hspace{120} of\ the\ 1st\ kind\ F(\phi,k)\\[10](1)\ F(\phi,k)={\large\int_{\small 0}^{\hspace{25}\small\phi}\frac{d\theta}{\sqrt{1-k^2sin^2\theta}}}\\\hspace{70}={\large\int_{\small 0}^{\hspace{25}\small x}\frac{dt}{\sqrt{(1-t^2)(1-k^2t^2)}}}\ ,\hspace{10}x=sin\phi\\$

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