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Question

Question: \(\int _ { 0 } ^ { 3 } | 2 - x | d x\) equals...

∫03∣2−x∣dx\int _ { 0 } ^ { 3 } | 2 - x | d x equals

A

2/7

B

5/2

C

3/2

D

−3/2- 3 / 2

Answer

5/2

Explanation

Solution

=∫02(2−x)dx+∫23−(2−x)dx= \int _ { 0 } ^ { 2 } ( 2 - x ) d x + \int _ { 2 } ^ { 3 } - ( 2 - x ) d x

=∫02(2−x)dx−∫23(2−x)dx=[2x−x22]02−[2x−x22]23= \int _ { 0 } ^ { 2 } ( 2 - x ) d x - \int _ { 2 } ^ { 3 } ( 2 - x ) d x = \left[ 2 x - \frac { x ^ { 2 } } { 2 } \right] _ { 0 } ^ { 2 } - \left[ 2 x - \frac { x ^ { 2 } } { 2 } \right] _ { 2 } ^ { 3 }

⇒I=[4−2]−[6−92−(4−2)]\Rightarrow I = [ 4 - 2 ] - \left[ 6 - \frac { 9 } { 2 } - ( 4 - 2 ) \right] =52= \frac { 5 } { 2 }.