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The value of int(1)^(4) |x-3|dx is equal...

The value of `int_(1)^(4) |x-3|dx` is equal to

A

2

B

`(5)/(2)`

C

`(1)/(2)`

D

`(3)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`int_(1)^(4)|x-3|dx`
`=int_(1)^(3)(3-x)dx+int_(3)^(4)(x-3)dx`
`=[3x-(x^(2))/(2)]_(1)^(3) +[(x^(2))/(2)-3x]_(3)^(4)`
`=(9-(9)/(2))-(3-(1)/(2))+((16)/(2)-12)-((9)/(2)-9)`
`=(5)/(2)`
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