<p>Let&nbsp;\(f(x) = \mathrm{e}^{2x}\cos{x}\), \(-1 \leq x \leq 2\).</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Show that&nbsp;\(f'(x) = \mathrm{e}^{2x}(2x \cos{x} - \sin{x})\).<span class="inline-marks">[3]</span></div></li></ol>
<p>Let the line \(L\) be the normal to the curve of \(f\) at \(x =0\).</p>
<ol class="abc-list" start="2"><li><div class="list-item-paragraph">Find the equation of \(L\).<span class="inline-marks">[5]</span></div></li></ol>
<p>The graph of \(f\) and the line \(L\) intersect at the point \( (0,1)\) and at a second point \(\mathrm{P}\).</p>
<ol class="abc-list" start="3"><li><ol class="i-list"><li><div class="list-item-paragraph">Find the \(x\)-coordinate of \(\mathrm{P}\).</div></li><li><div class="list-item-paragraph">Find the area of the region <strong>enclosed</strong> by the graph of \(f\) and the line \(L\).<span class="inline-marks">[6]</span></div></li></ol></li></ol>

Let \(f(x) = \mathrm{e}^{2x}\cos{x}\), \(-1 \leq x \leq 2\).

Show that \(f'(x) = \mathrm{e}^{2x}(2x \cos{x} - \sin{x})\).

Let the line \(L\) be the normal to the curve of \(f\) at \(x =0\).

The graph of \(f\) and the line \(L\) intersect at the point \( (0,1)\) and at a second point \(\mathrm{P}\).

Definite Integrals and Area under graph

International Baccalaureate Standard Level Mathematics