How do you find the arc length of the curve #x=y+y^3# over the interval [1,4]?
Christopher AgrestaI used WolframAlpha to do the integration:
From the reference Arc Length
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Isaiah AllenTo find the arc length of the curve (x=y+y^3) over the interval ([1,4]), follow these steps:
- Compute the derivative of (x) with respect to (y), which gives (dx/dy).
- Compute ((dx/dy)^2).
- Integrate (\sqrt{1 + (dx/dy)^2}) with respect to (y) over the interval ([1,4]).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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