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The value of int (1)^(2) (dx)/((x+1) sq...

The value of ` int _(1)^(2) (dx)/((x+1) sqrt((x^2)-1))` is

A

1

B

`1/(sqrt(3))`

C

`2/(sqrt(3))`

D

`(-2)/(sqrt(3))`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `l=int_(1)^(2)(dx)/((x+1)sqrt(x^(2)-1))` … (i)
Put `x=secthetarArrdx=sec thetatanthetad theta`
`thereforel=int_(0)^(pi//3)(sec thetatantheta)/((sectheta+1)tantheta)d theta=int_(0)^(pi//3)(1)/(1+cos theta)d theta`
`=int_(0)^(pi//3)("sec"^(2)(theta)/(2))/(2)d theta=(1)/(2)[("tan"(theta)/(2))/((1)/(2))]_(0)^(pi//3)=(1)/(sqrt(3))`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)
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