<ol class="abc-list"><li><div class="list-item-paragraph">By using the substitution $x=3\sec \theta $, evaluate $\int_{3\sqrt{2}}^{6}{\frac{3x+1}{\sqrt{{{x}^{2}}-9}}\mathrm{d}x}$ exactly.</div><p style="text-align: right;">[5]</p></li><li><div class="list-item-image"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/converted/1759840591539-fds9pxfm5n.jpg" alt="List item image" /></div><div class="list-item-paragraph">The diagram shows an ellipse with equation $\frac{{{x}^{2}}}{16}+\frac{{{\left( y-2 \right)}^{2}}}{4}=1$.</div><ol class="i-list"><li><div class="list-item-paragraph">Find the area of the shaded region, giving your answer correct to $3$ decimal places.</div><p style="text-align: right;">[2]</p></li><li><div class="list-item-paragraph">Find the exact volume of the solid generated when the shaded region is rotated $180{}^\circ $ about the $y$-axis.</div><p style="text-align: right;">[4]</p></li></ol></li></ol>

By using the substitution $x=3\sec \theta $, evaluate $\displaystyle\displaystyle \int_{3\sqrt{2}}^{6}{\frac{3x+1}{\sqrt{{{x}^{2}}-9}}\mathrm{d}x}$ exactly.

The diagram shows an ellipse with equation $\frac{{{x}^{2}}}{16}+\frac{{{\left( y-2 \right)}^{2}}}{4}=1$.

2017 YJC P1 Q9

2017 YJC P1 Q9

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