2022 ACJC J2 MYE Q2
(a)
If $1<a<b$, solve $\int_{0}^{b}{\left| a-{{x}^{2}} \right|}\text{ d}x$, leaving your answer in terms of $a$ and $b$.
[3]
(b)
Without the use of a graphic calculator, find the largest integer value of $n$ such that $\int_{\frac{n}{\text{e}}}^{{{\text{e}}^{\text{e}}}}{\frac{1}{x{{\left( \ln x \right)}^{2}}}}\text{ d}x$, where $1<\text{e}<n$, is positive.
[4]
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