Hobbies And Interests
Home  >> Science & Nature >> Science

How to Integrate a Spiral Around a Fixed Circumference

A spiral is a geometric shape similar to a circle. However, unlike a circle, the arc of a spiral curves inward and forms several interior loops before terminating at a central point. You can find the integral of a spiral around a fixed circumference in the same way you would find the integral of a circle. This is because you are integrating a circle at the same location as the fixed radius of the spiral. The integral of a circle is the area it encloses.

Things You'll Need

  • Calculator
Show More

Instructions

    • 1

      Familiarize yourself with the equations for a circle. The area equation of a circle is given by "Area = pi * radius^2," where the symbols "^2" means find the square of the number. The circumference of a circle is given by "Circumference = 2 * pi * radius."

    • 2

      Find the radius of a circle with the same circumference of a spiral loop. This requires the circumference equation. When you solve for the radius in this equation, you divide both sides of the equation by "2 * pi," in order to isolate the radius on one side of the equals sign. Suppose you have a circumference equal to "2 * pi." Dividing both sides yields a radius of 1.

    • 3

      Find the area of a circle with the same circumference as the spiral. This requires the area equation. Continuing with the example above, the area of a circle with a radius of 1 is equal to "pi," or roughly 3.14. This means the integral of a spiral around a fixed circumference of "2 * pi" is roughly equal to 3.14.


https://www.htfbw.com © Hobbies And Interests