Area under a curve given parametricallyEdexcel International A Level Maths: Mind map

Exam questions on Area under a curve given parametrically

1. A curve has parametric equations $x=t^2$, $y=4t$, for $t\ge0$. The region $R$ is bounded by the curve, the $x$-axis and the lines $x=1$ and $x=9$.
   The lines $x=1$ and $x=9$ are replaced by the $y$-axis and the line $x=4$. Find the area of the new region.2 marks
2. A curve has parametric equations $x=2t+1$, $y=t^2+2$, for $t\ge0$. The region $S$ is bounded by the curve, the $x$-axis and the lines $x=1$ and $x=7$.
   The lines $x=1$ and $x=7$ are replaced by the lines $x=3$ and $x=5$. Find the area of the new region.2 marks
3. One arch of a curve has parametric equations $x=2(t-\sin t)$, $y=2(1-\cos t)$ for $0\le t\le2\pi$. The region $R$ is bounded by this arch and the $x$-axis.
   Show that the area of $R$ is given by $\int_0^{2\pi}4(1-\cos t)^2\,dt$.3 marks