Find the arc length of a curve over an interval

In summary, the conversation discusses finding the arc length of a curve using integration and the use of a u substitution. There is also a suggestion to simplify the expression before using u substitution and a question about incorporating du/2y into the final answer.
  • #1
bocobuff
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0

Homework Statement


I'm trying to find the arc length of a curve over an interval and I've arrived at
[tex]\int[/tex] (y4 +2y2 +1)1/2 dy
and now I'm pretty sure i should use a u substitution in order to integrate.
I tried using u=y2 so du=2y dy so dy=du/2y
Then you have [tex]\int[/tex] (u2+2u+1)1/2 and eventually it boils down to [tex]\int[/tex] u+1 du which gives you u2/2 +u

But I think I forgot to incorporate the du/2y and I don't know if I can just change the answer to y2/2 + y.

Any thoughts?
 
Last edited:
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  • #2
You don't have to 'u sub' anything yet. First try and simplify (y^4+2*y^2+1)^(1/2). Isn't y^4+2*y^2+1=(y^2+1)^2? What's the (1/2) power of that?
 

What is the definition of arc length?

Arc length is the distance along a curved line, measured in units of length, such as inches or meters.

How is the arc length of a curve calculated?

The arc length of a curve is typically calculated using an integral, which is a mathematical tool used to find the area under a curve. The integral is evaluated over the interval of the curve's domain.

What is the difference between arc length and arc measure?

Arc length is a measurement of the distance along a curve, while arc measure is the angle subtended by an arc in a circle. Arc length is typically measured in units of length, while arc measure is measured in degrees or radians.

Can the arc length of a curve be negative?

No, the arc length of a curve cannot be negative. It is always a positive value, as it represents a distance along a curve.

What are some real-life applications of finding the arc length of a curve?

Finding the arc length of a curve is useful in various fields such as engineering, physics, and architecture. For example, it can be used to calculate the length of a curved road, the distance traveled by an object along a curved path, or the amount of material needed to construct a curved structure.

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