1-5-2-3-x-dx-

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

Facebook Tweet Pin