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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.

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

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

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