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Complete elliptic integral of the 1st kind K(k)

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Compute complete elliptic integral of the 1st kind K(k).
\(K(k)={\large\int_{\small 0}^{\frac{\pi}{2}}\frac{d\theta}{\sqrt{1-k^2sin^2\theta}}}\)
k 
-1≦k≦1
\(\normalsize Complete\ elliptic\ integral\\ \hspace{120px} of\ the\ 1st\ kind\ K(k)\\ (1)\ K(k)={\large\int_{\small 0}^{\frac{\pi}{2}}\frac{d\theta}{\sqrt{1-k^2sin^2\theta}}}\\ \hspace{60px}={\large\int_{\small 0}^{\small 1}\frac{dt}{\sqrt{(1-t^2)(1-k^2t^2)}}}\\\)

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