Finding Arc Length of c between (2,1,0) and (4,4,log2)

In summary, to find the arc length of the given path c, you will need to use the formula for arc length and set appropriate limits of integration. The lower limit will be (2, 1, 0) and the upper limit will be (4, 4, ln(2)). Solving for t in these points will give you the limits to use in the integral.
  • #1
aligshah88
2
0

Homework Statement




Let c be the path c(t)=(2t,t^2,logt), defined for t>0. Find the arc length of c between the points (2,1,0) and (4,4,log2)

I just have a problem with the limits for the integral...what limits so I set for it after finding the derivative and using Pythagorean theorem...thanks.
 
Physics news on Phys.org
  • #2
Let's start with the beginning, what's the formula for calculating the arc length??
 
  • #3
If your only problem is limits of integration, you want (2t, t^2,ln(t))= (2, 1, 0) for the lower limit, (2t, t^2, ln(t))= (4, 4, ln(2)). Can you solve 2t= 2 and 2t= 4? (Because those points on the curve, those values of t must satisfy t^2= 1, ln(t)= 0 and t^2= 4, ln(t)= 1, respectively.
 

1. What is the formula for finding the arc length?

The formula for finding the arc length is L = ∫√(1 + (dy/dx)^2) dx, where the integral is taken over the interval [a, b].

2. How do you calculate the arc length between two points?

To calculate the arc length between two points, you will need to first find the derivative of the function that defines the curve. Then, use the formula L = ∫√(1 + (dy/dx)^2) dx to find the integral between the two points.

3. Can I use the Pythagorean theorem to find the arc length?

No, the Pythagorean theorem cannot be used to find the arc length of a curve. It can only be used for finding the length of the hypotenuse of a right triangle.

4. What is the significance of the points (2,1,0) and (4,4,log2)?

These points represent the starting and ending points of the curve whose arc length is being calculated. The coordinates (2,1,0) represent the point where the curve starts and (4,4,log2) represents the point where it ends.

5. Can the arc length be negative?

No, the arc length cannot be negative. It is always a positive value that represents the distance along the curve between two points.

Similar threads

  • Calculus and Beyond Homework Help
Replies
3
Views
921
  • Calculus and Beyond Homework Help
Replies
1
Views
1K
  • Calculus and Beyond Homework Help
Replies
6
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
1K
Replies
7
Views
1K
  • Calculus and Beyond Homework Help
Replies
5
Views
1K
  • Calculus and Beyond Homework Help
Replies
7
Views
812
  • Calculus and Beyond Homework Help
Replies
5
Views
2K
Replies
6
Views
866
Back
Top