The profile of a specialized aerodynamic sail is modeled by a curve with parametric equations

\sqrt{36-6t}, \quad y = \frac{t^3}{\sqrt{36+6t}}, \quad 0 \le t \le 6

The curve intersects the $y$ -axis at the point where $t = 6$ and the $x$ -axis at the point where $t = 0$ . The region $R$ is bounded by the curve and the positive $x$ and $y$ axes.

Show that the area of $R$ is given by

\int_{0}^{6} \frac{t^3}{\sqrt{1296-36t^2}} \, dt

where $K$ is a constant to be found.

Using the substitution $u = 1296 - 36t^2$ , or otherwise, find the exact area of $R$ .

The profile of a specialized aerodynamic sail is modeled by a curve with parametric equations

\sqrt{36-6t}, \quad y = \frac{t^3}{\sqrt{36+6t}}, \quad 0 \le t \le 6

The curve intersects the $y$ -axis at the point where $t = 6$ and the $x$ -axis at the point where $t = 0$ . The region $R$ is bounded by the curve and the positive $x$ and $y$ axes.

Show that the area of $R$ is given by

\int_{0}^{6} \frac{t^3}{\sqrt{1296-36t^2}} \, dt

where $K$ is a constant to be found.

Using the substitution $u = 1296 - 36t^2$ , or otherwise, find the exact area of $R$ .

1 Pure Mathematics

Question 450

Markscheme

1 Pure Mathematics

Question 450

Markscheme

1 Pure Mathematics

Question 450

1 Pure Mathematics Questions

1 Pure Mathematics

Question 450

1 Pure Mathematics Questions