∫_0 ^(π/2) (((√(tanx)) sin^2 x)/((√(sin xcos x)) tan x))dx


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Question Number 54971 by peter frank last updated on 15/Feb/19

$\int_{0}^{\frac{π}{2}} \frac{\sqrt{t a n x} \sin^{2} x}{\sqrt{\sin x \cos x} \tan x} d x$
	Answered by kaivan.ahmadi last updated on 15/Feb/19

	$\int_{0}^{\frac{π}{2}} \frac{\sqrt{\frac{s i n x}{c o s x}} {s i n}^{2} x}{\sqrt{s i n x c o s x} \frac{s i n x}{c o s x}} d x =$ ${\int_{0}^{\frac{π}{2}} s i n x d x = - c o s x]}_{0}^{\frac{π}{2}} = 1$
	Answered by tanmay.chaudhury50@gmail.com last updated on 15/Feb/19

	$\int \frac{\sqrt{t a n x} \times {t a n}^{2} x \times {c o s}^{2} x}{\sqrt{t a n x \times {c o s}^{2} x} \times t a n x} d x$ $\int \frac{\sqrt{t a n x} \times t a n x \times c o s x}{\sqrt{t a n x}} d x$ $\int s i n x d x$ $= - ∣ c o s x ∣_{0}^{\frac{π}{2}}$ $= - (0 - 1) = 1 a n s$
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