<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Use the substitution $\tan y={{\mathrm{e}}^{x}}$ to find</span></div><div class="list-item-paragraph" style="text-align: center">$\int{\frac{1}{{{\mathrm{e}}^{x}}(1+{{\mathrm{e}}^{2x}})}\mathrm{d}x}$.</div><p style="text-align: right;">[4]</p></li><li><div class="list-item-content"><span class="list-item-text">The region bounded by the $x$-axis, the curve $y={{\mathrm{e}}^{{{x}^{2}}+1}}$, the lines $x=0$ and $x=1$ is rotated about the $y$-axis to form a solid of revolution of volume $V$ . Find the exact value of $V$.</span></div><p style="text-align: right;">[6]</p></li></ol>

Use the substitution $\tan y={{\mathrm{e}}^{x}}$ to find

$\displaystyle\displaystyle \int{\frac{1}{{{\mathrm{e}}^{x}}(1+{{\mathrm{e}}^{2x}})}\mathrm{d}x}$.

The region bounded by the $x$-axis, the curve $y={{\mathrm{e}}^{{{x}^{2}}+1}}$, the lines $x=0$ and $x=1$ is rotated about the $y$-axis to form a solid of revolution of volume $V$ . Find the exact value of $V$.

2012 RVHS P2 Q2

2012 RVHS P2 Q2

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