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Question: The value of \(\int _ { 1 } ^ { 5 } ( | x - 3 | + | 1 - x | ) d x\) is...

The value of ∫15(∣x−3∣+∣1−x∣)dx\int _ { 1 } ^ { 5 } ( | x - 3 | + | 1 - x | ) d x is

A

10

B

56\frac { 5 } { 6 }

C

21

D

12

Answer

12

Explanation

Solution

∫15(∣x−3∣+∣1−x∣)dx\int _ { 1 } ^ { 5 } ( | x - 3 | + | 1 - x | ) d x =∫15∣x−3∣dx+∫15∣1−x∣dx= \int _ { 1 } ^ { 5 } | x - 3 | d x + \int _ { 1 } ^ { 5 } | 1 - x | d x

=12= 12.