Arc Length Need Verification, If Wrong, Can You Help?

In summary, arc length is the distance along a curved line or arc and is typically measured in units such as meters or feet. It is important to verify arc length to ensure accuracy and avoid errors in calculations or design. This can be done using mathematical formulas or physical measurements. If the arc length is incorrect, it can lead to miscalculations and errors, but a scientist can offer guidance and assistance in verifying and correcting the measurement. Ultimately, the responsibility falls on the person who made the initial measurement.
  • #1
zcabral
30
0

Homework Statement



Length of curve: y=1/2(ex-e-x) from 0 to 2


Homework Equations



s = ∫√[1+(dy/dx)^2] dx

The Attempt at a Solution



[sqrt(4+2e^(-x)+e^x)]*[-1+e^x]/[1+e^x].
= 3.323971
 
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  • #2
Your notation is ambiguous. I'm guessing that your curve is,

[tex]y(x) = \frac{e^x-e^{-x}}{2}[/tex]

In which case it may be useful to note that,

[tex]\frac{e^x-e^{-x}}{2} = \sinh(x)[/tex]

Which (along with a hyperbolic identity) would greatly simplify your integrand.
 

1. What is arc length?

Arc length is the distance along a curved line or arc. It is typically measured in units such as meters or feet.

2. Why is it important to verify arc length?

Verifying arc length ensures that the measurement is accurate and helps to avoid errors in calculations or design.

3. How can I verify arc length?

Arc length can be verified by using mathematical formulas or by physically measuring the curve with a ruler or tape measure.

4. What happens if the arc length is wrong?

If the arc length is incorrect, it can lead to miscalculations and errors in design or analysis. It is important to double check and verify the measurement to ensure accuracy.

5. Can you help if the arc length is wrong?

As a scientist, I can provide guidance on how to verify the arc length and offer assistance in correcting any errors. However, the responsibility for verifying and correcting the measurement ultimately falls on the person who made the initial measurement.

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