Consider the region, R, bounded by the x-axis, the y-axis, and the graphs of the equations y=1/(x^2+1) and y=lnx

Question

Find the area of the region R.

a. 5.497
b. 1.483
c. 0.879
d. 0.013

Answer 1

The integral breaks into two parts that must be added. The first part is the integral from 0 to 1 ∫dx/(1+x²) = 0.785.

the second part is the integral from 1 to the intersection point of the two curves which is about 1.4

 

 ∫((1/(1+x²)-ln(x))dx =0.094

 

The sum is about 0.879. So answer c) is correct