calculate ∫_0 ^(π/6) ∣ cos(2x)−cos(3x)∣dx


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Question Number 39834 by math khazana by abdo last updated on 12/Jul/18

$c a l c u l a t e \int_{0}^{\frac{π}{6}} ∣ c o s (2 x) - c o s (3 x) ∣ d x$
	Answered by tanmay.chaudhury50@gmail.com last updated on 12/Jul/18

	$\int_{0}^{\frac{Π}{6}} (c o s 2 x - c o s 3 x) d x$ $r e a s o n v a l u e o f c o s 2 x > c o s 3 x i n [0, \frac{Π}{6}]$ $=∣ \frac{s i n 2 x}{2} - \frac{s i n 3 x}{3} ∣_{0}^{\frac{Π}{6}}$ $= (\frac{s i n \frac{Π}{3}}{2} - \frac{s i n \frac{Π}{2}}{3}) = \frac{\sqrt{3}}{4} - \frac{1}{3} = \frac{3 \sqrt{3} - 4}{12}$
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