Question

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)`

Answer 1

Correct Answer - 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)`