Home page for accesible maths 3 Chapter 3 contents 3.13 Simpson’s Rule 3.15 Table for Simpson’s rule

Style control - access keys in brackets

Font (2 3) - + Letter spacing (4 5) - + Word spacing (6 7) - + Line spacing (8 9) - +

3.14 Perimeter of a particular ellipse

Example.

Use Simpson’s rule to estimate the perimeter of the ellipse

\left(\frac{x}{5}\right)^{2}+\left(\frac{y}{3}\right)^{2}=1.

In this case $a={5}$ and $b={3,}$ so that

\kappa=\sqrt{1-\frac{b^{2}}{a^{2}}}=\,{\sqrt{1-\frac{9}{25}}=}\,{\sqrt{\frac{1% 6}{25}}=\frac{4}{5}.}

By Prop. 3.11, the perimeter of the ellipse is $20E({\frac{4}{5}})$ . (You are not expected to remember Prop. 3.11, but you could otherwise answer this question by parametrizing the ellipse via $x=5\sin t$ , $y=3\cos t$ .)

We therefore apply Simpson’s rule to estimate $E(\frac{4}{5})$ .