find the value of ∫_(π/3) ^(π/2) (dx/(√(2cos^2 x +3sin^2 x)))


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Question Number 57817 by Abdo msup. last updated on 12/Apr/19

$f i n d t h e v a l u e o f \int_{\frac{π}{3}}^{\frac{π}{2}} \frac{d x}{\sqrt{2 {c o s}^{2} x + 3 {s i n}^{2} x}}$
Commented by mr W last updated on 13/Apr/19
Incomplete elliptic integral of the first kind, no elementary solution.
	Answered by tanmay.chaudhury50@gmail.com last updated on 13/Apr/19

	$2 {c o s}^{2} x + 3 {s i n}^{2} x$ $= 2 + {s i n}^{2} x$ $= 2 + \frac{1 - c o s 2 x}{2}$ $= \frac{5 - c o s 2 x}{2}$ $\int_{\frac{π}{3}}^{\frac{π}{2}} \frac{\sqrt{2} d x}{\sqrt{5 - c o s 2 x}}$ $n o w . . . \int \frac{d x}{\sqrt{a + b c o s x}} f o r m a t . . . w a i t . . .$
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