find F(a)=∫_0 ^1 (√((1+a^2 t^2 )/(1−t^2 ))) dt for background see Q127811.


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Question Number 127925 by mr W last updated on 03/Jan/21

$f i n d F (a) = \int_{0}^{1} \sqrt{\frac{1 + a^{2} t^{2}}{1 - t^{2}}} d t$ $f o r b a c k g r o u n d s e e Q 127811 .$
	Answered by mindispower last updated on 03/Jan/21

	$= \int_{0}^{1} \sqrt{\frac{1 - (- {(a)}^{2}) t^{2}}{1 - t^{2}}} d t = E (1 ∣ - a^{2})$ $E e l e p t i c i n t e g r a l o f 2 n d k i n d$ $E (x ∣ k^{2}) = \int_{0}^{x} \frac{\sqrt{1 - k^{2} t^{2}}}{\sqrt{1 - t^{2}}} d t$
	Commented by mr W last updated on 03/Jan/21

	$t h a n k s s i r!$
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