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- Thread starter swal
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- Joined
- Nov 19, 2021

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- 458

YesThat's an integral over x, I presume?

-Dan

The function is a relation - I'm trying to find the length of the curve of this function:

Where a is 2.95 and b is 2. I need the length of the curve between -2.95 and 2.95, given y is greater than or equal to zero.This can be rearranged as:

This can be implicitly differentiated in order to substitute into the formula for the length of an arc, but I can't do the integration.

- Joined
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Take the square root?This can be implicitly differentiated in order to substitute into the formula for the length of an arc, but I can't do the integration.

[math]y=\pm \sqrt{\left(1-\frac{x^2}{a^2}\right)\frac{b^2}{1+kx}}[/math]

Take the positive only.y is greater than or equal to zero

[math]y=\sqrt{\left(1-\frac{x^2}{a^2}\right)\frac{b^2}{1+kx}}[/math]First, I would simplify then find the derivative. But it does not look pretty...

Last edited:

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The integrand must be a function of x; implicit differentiation doesn't initially produce that, because you still have y in the derivative. You need to replace y with its expression in terms of x (BBB's radical) before integrating. (Assuming the rest of your work is correct, which I haven't looked at.)The function is a relation - I'm trying to find the length of the curve of this function:

View attachment 30672

Where a is 2.95 and b is 2. I need the length of the curve between -2.95 and 2.95, given y is greater than or equal to zero.This can be rearranged as: View attachment 30673

This can be implicitly differentiated in order to substitute into the formula for the length of an arc, but I can't do the integration.

Not all functions can be integrated exactly, or with a reasonable amount of work! This may well be one of the many that would need numerical integration.

- Joined
- Nov 19, 2021

- Messages
- 458

- Joined
- Nov 19, 2021

- Messages
- 458

I doubt even WolframAlpha can. You won't get any further until you show us the exact original question.ok, so I've done that. Can anyone integrate this with respect to x in order to find k?

View attachment 30688