To determine

To find:

Area between the given curves.

Answer

0.06598

Explanation

Given: y==ln⁡xx and y=ln⁡x2x.

Blue coloured graph represents the function fx=ln⁡xx and the green coloured graph represents the function gx=(ln⁡x)2x.

The required area is given by:A=∫12.71fx-gxdx=∫12.71ln⁡xx -(ln⁡x)2xdx=∫12.71ln⁡xx dx–∫12.71(ln⁡x)2xdx. Substitute ln⁡x=t, then 1xdx=dt. Also, x=1  implies t=0, and x=2.71 implies t=ln⁡2.71. Thus,∫t=0ln⁡2.71tdt-∫t=0ln⁡2.71t2dt=0.06598.

Conclusion:

We could calculate the area between the 2 given curves as  0.06598.