Let's say I have a parabola that I know the equation of. I then asked myself the question "how do I calculate the length of the curve between two values of x, for example.(adsbygoogle = window.adsbygoogle || []).push({});

After thinking about it, I realised I could use pythagoras: √δx + δy will give me a length, and then I could find the sum of these lengths to give the length of the curve. However, given that δx is 'infinitessimally small,' I would have to add and infinite number of lengths to get the length of the curve.

For example:

given [itex]y = x^{2}[/itex] find the length of the curve while [itex]-2 \leq x \leq 2[/itex]

so then (assuming my idea is correct), it will be:

The sum of [itex]\sqrt{\delta x + (\delta x)^{2}}[/itex] for all values of x between -2 and 2.

Am I along the right lines here? And if so, how do I calculate this 'infinite sum.'

I really would like to figure this out myself, so if (as i'm sure there is) a way to calculate this, then please don't tell me it. Some pointers would be great though!

Many thanks

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Calculating the length of a curve

Loading...

Similar Threads - Calculating length curve | Date |
---|---|

B Calculate probability of getting 2 red balls | Mar 2, 2018 |

How to calculate length of arc? | Jan 17, 2013 |

How to calculate arc length in unit circle | Dec 7, 2011 |

How does one calculate the distance (or length) on the ground | Oct 25, 2008 |

Numerical calculation about curve length | Sep 2, 2007 |

**Physics Forums - The Fusion of Science and Community**