Area bounded by `f(x)=(x^(2)-1)/(x^(2)+1)` and the line y = 1 is

Options

A. `pi` sq. units
B. `2pi` sq. units
C. `pi//2` sq. units
D. none of these

Answer

B

Explanation

`y=f(x)=(x^(2)-1)/(x^(2)+1)=1-(2)/(x^(2)+1)`
`y=0," "therefore (x^(2)-1)/(x^(2)+1)=0 or x = pm1`
Also function is even.
y(0) = -1 is the minimum value of function.
`underset(xrarrpmoo)(lim)(1-(2)/(x^(2)+1))=1`
The graph of the function is as shown in the following figure:

`A=2int_(0)^(oo)(1-(x^(2)-1)/(x^(2)+1))dx`
`=4int_(0)^(oo)(dx)/(x^(2)+1)`
`=4.tan^(-1)|_(0)^(oo)=4.(pi)/(2)=2pi`