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Choose the correct answer int0 2/3(dx)/(...

Choose the correct answer `int0 2/3(dx)/(4+9x^2)` (A) `pi/6` (B) `pi/(12)` (C) `pi/(24)` (D) `pi/4`

Text Solution

Verified by Experts

The correct Answer is:
c
`int_(0)^(2//3)(1)/(4+9x^(2))dx`
`=(1)/(9)int_(0)^(2//3)(1)/((4)/(9)+x^(2))dx`
`=(1)/(9)int_(0)^(2//3)(1)/(((2)/(3))^(2)+x^(2))dx`
`=(1)/(9).(1)/(2//3)[tan^(-1)((x)/(2//3))]_(0)^(2//3)`
`=(1)/(6)[tan^(-1)((3x)/(2))]_(0)^(2//3)`
`=(1)/(6)[tan^(-1)((3)/(2).(2)/(3))-tan^(-1)0]`
`=(1)/(6) (tan^(-1)1-0)=(1)/(6).(pi)/(4)=(pi)/(24)`
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