<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">If $1 < a < b$, solve $\int_{0}^{b}{\left| a-{{x}^{2}} \right|}\mathrm{ d}x$, leaving your answer in terms of $a$ and $b$.</span></div><p style="text-align: right;">[3]</p></li><li><div class="list-item-content"><span class="list-item-text">Without the use of a graphic calculator, find the largest integer value of $n$ such that $\int_{\frac{n}{\mathrm{e}}}^{{{\mathrm{e}}^{\mathrm{e}}}}{\frac{1}{x{{\left( \ln x \right)}^{2}}}}\mathrm{ d}x$, where $1 < \mathrm{e} < n$, is positive.</span></div><p style="text-align: right;">[4]</p></li></ol>

If $1 < a < b$, solve $\displaystyle\displaystyle \int_{0}^{b}{\left| a-{{x}^{2}} \right|}\mathrm{ d}x$, leaving your answer in terms of $a$ and $b$.

Without the use of a graphic calculator, find the largest integer value of $n$ such that $\displaystyle\displaystyle \int_{\frac{n}{\mathrm{e}}}^{{{\mathrm{e}}^{\mathrm{e}}}}{\frac{1}{x{{\left( \ln x \right)}^{2}}}}\mathrm{ d}x$, where $1 < \mathrm{e} < n$, is positive.

2022 ACJC J2 MYE Q2

2022 ACJC J2 MYE Q2

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