Question
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:onsider the curve for . Find the arc length of the curve.

Ask by Gough Edwards. in the United States
Jan 25,2025

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Answer

The arc length of the curve from to is units.

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The Deep Dive

To find the arc length of the curve given by from to , we can use the formula for the arc length of a curve defined as :
  1. First, we need to compute the derivative :
  2. Next, square the derivative:
  3. Now, we will use the arc length formula:
    Which simplifies to:
    This further simplifies to:
  4. We can write:
Using the identity , this way we can explore a simpler integral if possible.
  1. The final integral can be calculated either analytically or numerically over the evaluated limits from to .
After solving, the arc length evaluates to:
Eventually, computing all the terms will provide the arc length of the curve from to .
Therefore, the arc length, when calculated completely, is found to be:
after simplification and evaluation of constants.

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