Line Integral: Evaluating Along Circular Path from P1 to P2

In summary, the problem requires evaluating a line integral along a quarter of a circular path with a radius of 3, from the y-axis to the x-axis. The equation to integrate is E = (x)x - (y)y, where the variables in the parentheses represent the direction. The expression dl still needs to be determined.
  • #1
Cryphonus
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0

Homework Statement



Evaluate the line integral along the segment P1(0,3) to P2(-3,0) of the circular path shown in figure.

Figure basically shows a circle with a radius of 3. The part that i have to evaluate is from the y-axis (P1) to the x-axis (P2), basically a quarter of the circle.



Homework Equations



integral from P1 to P2 of E.dl



The Attempt at a Solution



I just can't write the equation to begin with.

i would be glad if you can give me some hints about the equation that i have to integrate, thanks a lot!
 
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  • #2
Cryphonus said:

Homework Statement



Evaluate the line integral along the segment P1(0,3) to P2(-3,0) of the circular path shown in figure.

Figure basically shows a circle with a radius of 3. The part that i have to evaluate is from the y-axis (P1) to the x-axis (P2), basically a quarter of the circle.



Homework Equations



integral from P1 to P2 of E.dl



The Attempt at a Solution



I just can't write the equation to begin with.

i would be glad if you can give me some hints about the equation that i have to integrate, thanks a lot!

I'm afraid there aren't any mind readers here. If you can't write down the equation you need help with, how are we to help you figure out how to work it?
 
  • #3
oh sorry i thought it was there E= (x) x - (y) y variables in the paranthesis refers to the direction. i still need to express dl somehow.
 

1. What is a line integral?

A line integral is a mathematical concept used to calculate the total value of a function along a specific path. It involves breaking down a curved or complex path into smaller segments and summing up the values of the function at each segment.

2. What is the significance of evaluating along a circular path?

By evaluating a line integral along a circular path, we can calculate the total value of a function over a closed loop. This is particularly useful in physics and engineering, where many physical laws are based on the conservation of energy over a closed path.

3. How do you calculate a line integral along a circular path?

To calculate a line integral along a circular path, we use a specific formula that takes into account the radius of the circle, the angle of rotation, and the function being evaluated. This formula can be derived from the fundamental theorem of calculus and involves taking the derivative of the function along the path.

4. What is the difference between a line integral and a regular integral?

While a regular integral calculates the area under a curve on a Cartesian plane, a line integral calculates the value of a function along a specific path. This path can be curved or complex, unlike a regular integral which is calculated along a straight line.

5. How is a line integral used in real-world applications?

Line integrals have various applications in physics, engineering, and economics. For example, in physics, line integrals are used to calculate the work done by a force along a curved path. In engineering, they are used to calculate the flow of a fluid along a particular path. In economics, they are used to calculate the total value of a function over a specific time period.

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