Area of circle using integration

Click For Summary
To find the area of a circle using integration, the width must be expressed in terms of height. The Pythagorean theorem is applied, where the vertical leg represents the height from the circle's center to a horizontal strip, and the horizontal leg is half the width of that strip. The hypotenuse corresponds to the circle's radius. The equation provided, w = 2√(3² - h²), correctly describes width in terms of height. Understanding this relationship is crucial for setting up the integration to calculate the area.
PhysicsBoyMan
Messages
33
Reaction score
0

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?
 
Last edited by a moderator:
Physics news on Phys.org
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:
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

Similar threads

  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 7 ·
Replies
7
Views
1K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 12 ·
Replies
12
Views
2K
Replies
5
Views
2K
  • · Replies 10 ·
Replies
10
Views
5K