The curve $C$ is defined by the parametric equations $x=6t-1$, $y=8{{t}^{2}}+2$ where \(t

Question

The curve $C$ is defined by the parametric equations $x=6t-1$, $y=8{{t}^{2}}+2$ where $t\ge \frac{1}{6}$. The line $N$, with equation $3y=8x-10$, is the tangent to $C$ at the point $\left( 5,10 \right)$. The region enclosed by $C$, $N$ and the $y$-axis is denoted by $R$. Find the area of $R$. Find the cartesian equation of $C$. Hence, find the volume generated when $R$ is rotated about the $y$-axis through ${{360}^{\circ }}$.

Accepted Answer

(a) 250/27 units²; (b) 152 units³ (3 s.f.)

NYJC Applications of Integration Tutorial Q1

NYJC Applications of Integration Tutorial Q1

Video Solution:

Solution:

Solution locked