Integral Calculation of the content of a planar shape bounded by curves.
Checking the result. I'd like to check my progress. Input Calculation of the content of a planar shape bounded by curves for x = 0, x = 1, y = x * ln (x), y = -2xln (x) It sent me 3/4.
The only issue I have with your solution is the implicit claim that $$\lim_{x \to 0^+} \frac{x^2}{2} \log x = 0,$$ which you assumed when you computed $$\left[\frac{x^2}{2} \log x \right]_{x=0}^1.$$ To justify this rigorously, you would need to have previously established the value of this limit, or prove it in your solution; e.g., via L'Hopital's rule or some other method.