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I am looking for the area between

\[f(x)=x\cdot ln^{2}(x)-x\]

and the x-axis.

I have a solution in hand, it suggests that the area is:

\[\int_{\frac{1}{e}}^{e}(x-x\cdot ln^{2}(x))dx\approx 1.95\]

I have a problem with this solution, I don't understand where the area between 0 and 1/e had gone to...

I plotted the function in maple, and an area is appearing very clearly (see photo).

So my question: Do you think like me, that the solution attached to this exercise is wrong? If not, where does this area gone to ?

thanks !