<p>The curve $C$ has parametric equations</p>
<p style="text-align: center">$x={{t}^{3}}-t,y={{\mathrm{e}}^{t}},\mathrm{for }t\ge -1.$</p>
<ol class="i-list"><li><div class="list-item-paragraph">Sketch $C$, labelling all axial intercept(s).</div><p style="text-align: right;">[2]</p></li><li><div class="list-item-paragraph">Find the equation of the tangent to the curve when $t=1$, leaving your answer in terms of $e$.</div><p style="text-align: right;">[3]</p></li><li><div class="list-item-paragraph">The normal to the curve $C$ at point $P\left( {{p}^{3}}-p,{{\mathrm{e}}^{p}} \right)$ is parallel to the $x$-axis and intersects the $y$-axis at point $S\left( 0,s \right)$, where$s<1$. Find the exact value of $p$.</div><p style="text-align: right;">[2]</p></li><li><div class="list-item-paragraph">Find the area of the region bounded by the curve $C$ and the $y$-axis.</div><p style="text-align: right;">[3]</p></li></ol>

$x={{t}^{3}}-t,y={{\mathrm{e}}^{t}},\mathrm{for }t\ge -1.$

Sketch $C$, labelling all axial intercept(s).

Find the equation of the tangent to the curve when $t=1$, leaving your answer in terms of $e$.

The normal to the curve $C$ at point $P\left( {{p}^{3}}-p,{{\mathrm{e}}^{p}} \right)$ is parallel to the $x$-axis and intersects the $y$-axis at point $S\left( 0,s \right)$, where$s<1$. Find the exact value of $p$.

Find the area of the region bounded by the curve $C$ and the $y$-axis.

Applications of Intergration - General

Applications of Intergration

H2 Math

International Baccalaureate Higher Level Mathematics

2013 NJC P1 P8

2013 NJC P1 P8

Video Solution: