Integrals with a circle in the middle of them

In summary, the conversation discusses the area under a circle, how to calculate the integral with a circle in the middle, the purpose of integrating with a circle in the middle, and real-life applications of integrals with a circle in the middle. It is mentioned that the area under a circle is equal to the product of pi and the radius squared, and that the integral can be solved using basic geometry. The purpose of integrating with a circle in the middle is to find the area under a circle, which has various applications in physics and engineering. Additionally, it is noted that integrals with a circle in the middle have real-life applications in fields such as engineering, physics, and astronomy.
  • #1
PainDoc
2
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What is the symbol of an integral with a circle in the middle called? I am asking because Gauss's Law is defined to be equal to that integral of the dot product of E and dA.
 
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  • #2
PainDoc said:
What is the symbol of an integral with a circle in the middle called? I am asking because Gauss's Law is defined to be equal to that integral of the dot product of E and dA.
The symbol

[tex] \oint_s \ldots d\mathbold{x}[/tex]

is often used to indicate that the contour over which the integral is being taken is closed.
 

1. What is the area under a circle?

The area under a circle is equal to the product of pi (π) and the radius squared (πr^2).

2. How do you calculate the integral with a circle in the middle?

To calculate the integral with a circle in the middle, you can use the formula for the area under a circle (πr^2) and integrate it with respect to the variable in the integral.

3. What is the purpose of integrating with a circle in the middle?

The purpose of integrating with a circle in the middle is to find the area under a circle, which can be used in various applications in physics and engineering.

4. Can the integral with a circle in the middle be solved using basic geometry?

Yes, the integral with a circle in the middle can be solved using basic geometry by finding the area of the circle and then integrating it with respect to the variable in the integral.

5. Are there any real-life applications of integrals with a circle in the middle?

Yes, integrals with a circle in the middle have real-life applications in fields such as engineering, physics, and astronomy, where finding the area under a circular shape is necessary for calculations and designs.

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