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11.5 Integration by Substitution

Question 4

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.

[4]

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

[7]

Markscheme

11.5 Integration by Substitution Questions

A Level
Maths
11.5 Integration by Substitution

59 exam-style questions on Edexcel A Level Maths 11.5 Integration by Substitution. Each one has a worked solution and a mark scheme showing where the marks go.

11.5 Integration by Substitution

Question bank

11.5 Integration by Substitution

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Question 4

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.

[4]

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

[7]

Markscheme

11.5 Integration by Substitution Questions

A Level
Maths
11.5 Integration by Substitution

59 exam-style questions on Edexcel A Level Maths 11.5 Integration by Substitution. Each one has a worked solution and a mark scheme showing where the marks go.