!How to find the exact area of this region? (1 Viewer)

[fabl]

How to find the exact area of this region that lies below 1/ (4x^2 +1) and above 1/(x^2 +4)?

 

[photastic]

First graph the two functions to see which one is the top and bottom function and also the point of intersection. In this, the point of intersections are 1 and 1, by solving for x and in this region, the first function is above the second function.

So solve a definite integral between -1 and 1 for 1/ (4x^2 +1) minus 1/(x^2 +4). Or since they are both even functions, you can also multiply the definite integral between 0 and 1 for 1/ (4x^2 +1) minus 1/(x^2 +4) by 2.

Ceebs doing it myself but the link is the integral working out.

https://www.symbolab.com/solver/def...x^{2}+1}-\frac{1}{x^{2}+4}dx/?origin=enterkey