The document computes the area of a region bounded by the functions y=5/4 and y=1/(1-x^2). It sets the two functions equal to find the bounds of x as -3/5 and 3/5. It then calculates the area by integrating 1/(1-x^2) from -3/5 to 3/5, which is equal to 2sin-1(3/5).

1. Compute the area of the following region:
The region bounded by y=5/4 and y=1/(1-x2)
Solution
The region bounded by y=5/4 and y=1/(1-x2)
5/4=1/(1-x2)
16/25=1-x2
x^2=9/25
x=-3/5,3/5
so integrating from -3/5 to 3/5 1/(1-x2) will five the required area
integrating from -3/5 to 3/5 1/(1-x2) dx
put x=sin t
1-x^2=cos^2 t
dx=cos t
so -3/5 to 3/5 sin-1 x
area is 2sin-1(3/5)