Find the area of the region bounded by the graphs of the given curves

Question

y=x/3 and x/(x^2+1)

Answer 1

The region is bounded by the intersection points from x/(x²+1) = x/3 x = 0 and sqrt(2)

The area between the curves is found from the integral of:

(x/(x²+1) - x/3) dx from 0 to sqrt(2) or

1/2 * ln(x²+1) - x²/6 from 0 to sqer(2) = 1/2 * ln(3) - 1/3