Area of circle using integration

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SUMMARY

The discussion focuses on calculating the area of a circle using integration, specifically through the relationship between width and height. The equation provided, w = 2√(3² - h²), illustrates how to express width in terms of height, utilizing the Pythagorean theorem. Participants clarify that the triangle formed is not visually apparent but is essential for understanding the integration process. The conversation emphasizes the importance of correctly interpreting geometric relationships in calculus.

PREREQUISITES
  • Understanding of basic calculus concepts, particularly integration.
  • Familiarity with the Pythagorean theorem and its application in geometry.
  • Knowledge of circle geometry and properties, including radius and diameter.
  • Ability to manipulate algebraic equations, specifically solving for variables.
NEXT STEPS
  • Study the derivation of the area of a circle using integration techniques.
  • Learn how to apply the Pythagorean theorem in various geometric contexts.
  • Explore advanced calculus topics, such as polar coordinates and their applications in area calculations.
  • Investigate other methods of calculating areas of irregular shapes using integration.
USEFUL FOR

Students studying calculus, educators teaching geometry and integration, and anyone interested in applying mathematical concepts to solve real-world problems involving circular shapes.

PhysicsBoyMan
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Homework Statement


http://postimage.org/]Screen_Shot_2016_01_09_at_10_13_38_AM.png[/PLAIN]
free picture upload


2. The attempt at a solution
I want to go width times delta height. To do this I must describe width in terms of height.

Here they used the Pythagorean theorem which is weird to me because I don't see a nice triangle. Where h meets w the triangle extends outside of the circle. We divide w by 2 I guess to treat it as like a radius?

I guess my question is how do I describe width in terms of height in this context?
 
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PhysicsBoyMan said:

Homework Statement


Screen_Shot_2016_01_09_at_10_13_38_AM.png[/PLAIN]
free picture upload


2. The attempt at a solution
I want to go width times delta height. To do this I must describe width in terms of height.

Here they used the Pythagorean theorem which is weird to me because I don't see a nice triangle.
The triangle isn't shown in the picture. The vertical leg of the triangle goes from the center up to the horizontal strip. The horizontal leg is half the width of the strip. The hypotenuse is the radius of the circle.
PhysicsBoyMan said:
Where h meets w the triangle extends outside of the circle. We divide w by 2 I guess to treat it as like a radius?
No. See above.
PhysicsBoyMan said:
I guess my question is how do I describe width in terms of height in this context?
They already give you w in terms of h in the equation ##w = 2\sqrt{3^2 - h^2}.##
 
Last edited by a moderator:

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