∫_1 ^5 ∣2−∣3−x∣∣dx


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Question Number 151860 by maged last updated on 23/Aug/21

$\underset{1}{\int^{5}} ∣ 2 - ∣ 3 - x ∣∣ dx$
Commented by lyubita last updated on 23/Aug/21

$I t m e a n s a r e a b o u n d e d b y t h e g r a p h$ $a n d x a x i s b e t w e e n x = 1 a n d x = 5$
Commented by lyubita last updated on 23/Aug/21

Commented by maged last updated on 23/Aug/21

$Thank you$
	Answered by puissant last updated on 23/Aug/21

	$Q = \int_{1}^{5} ∣ 2 - ∣ 3 - x ∣∣ d x$ $= \int_{1}^{3} ∣ 2 - 3 + x ∣ d x + \int_{3}^{5} ∣ 2 + 3 - x ∣ d x$ $= \int_{1}^{3} ∣ x - 1 ∣ d x + \int_{3}^{5} ∣ 5 - x ∣ d x$ $= {[\frac{x^{2}}{2} - x]}_{1}^{3} + {[5 x - \frac{x^{2}}{2}]}_{3}^{5}$ $= [(\frac{9}{2} - 3) - (\frac{1}{2} - 1)] + [(25 - \frac{25}{2}) - (15 - \frac{9}{2})]$ $= 2 + 2$ $= 4$ $∴∵ Q = \int_{1}^{5} ∣ 2 - ∣ 3 - x ∣∣ d x = 4 . .$
	Commented by maged last updated on 23/Aug/21

	$thank you$
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