Polar area between two equations

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In summary, the conversation discusses using polar coordinates to find the area shared by two curves and the equation used for the solution. The person is unsure about the limits of integration and asks for help. The thread is marked as solved, but the solution is not provided.
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[SOLVED] Polar area between two equations

Homework Statement



Using polar coordinates, find the area of the region shared by both curves [2cos(theta) and 2sin(theta)]


Homework Equations


.5integral((2cos(theta) - 2sin(theta))^2)dtheta)


The Attempt at a Solution



Ok. So I know what equation I have to use. I also know that one of the limits of integration will be pi/4 (the point that's not on the origin). However, I don't know what theta value represents the point on the origin. I may be doing this all wrong. Any help is appreciated.
 
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Why is this thread marked "[Solved]"?
 

FAQ: Polar area between two equations

What is the polar area between two equations?

The polar area between two equations refers to the region enclosed by the two polar curves when graphed on a polar coordinate plane.

How is the polar area between two equations calculated?

To calculate the polar area between two equations, the first step is to find the points of intersection between the two curves. Then, use the formula A = 1/2 ∫(r_2^2 - r_1^2) dθ, where r_1 and r_2 are the equations of the two curves and dθ represents the change in angle between the two points of intersection.

Can the polar area between two equations be negative?

No, the polar area between two equations cannot be negative. The area is always represented as a positive value, as it is a measure of the enclosed region.

What are some real-world applications of finding the polar area between two equations?

Finding the polar area between two equations can be used in various fields such as physics, engineering, and geography. Some examples include calculating the area of a circular field, determining the volume of a cone, and measuring the distance between two cities on a globe.

Are there any shortcuts or tricks for finding the polar area between two equations?

Yes, there are some shortcuts that can be used to find the polar area between two equations. For example, if the two curves are symmetric about the origin, the area can be calculated by multiplying the area of one portion by two. Additionally, if the two curves have symmetry along the x-axis, the area can be found by doubling the integral from 0 to the point of intersection.

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