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Let f(x) = " max " {3,x^(2),(1)/(x^(2))}...

Let `f(x) = " max " {3,x^(2),(1)/(x^(2))}` for `(1)/(2) le x le 2`. Then the value of integral `int_(1//2)^(2)f(x) dx` is

A

`(11)/(3)`

B

`(13)/(3)`

C

`(14)/(3)`

D

`(16)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
Given Integral can be distributed ito
`int_(1//2)^(1//sqrt(3))(1)/(x^(2)).dx+ int_(1//sqrt(3))^(sqrt(3))3dx+ int_(sqrt(3))^(2)x^(2).dx=(14)/(3)`
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