Ok, I have the following problem find the area inside the cardioid
and outside the circle
I know you check for the limits of integration by finding where the two graphs intersect which is
However they show how the solution is done im a trying to re work it and they say you can just take the area of half the region and multiply it by two which gives the these limits of integration
How the hell that came up? I cant see where the right half the graph starts at -pi/2
Originally Posted by RockHard
Ok, I have the following problem find the area inside the cardioid
and outside the circle
I know you check for the limits of integration by finding where the two graphs intersect which is
However they show how the solution is done im a trying to re work it and they say you can just take the area of half the region and multiply it by two which gives the these limits of integration
How the hell that came up? I cant see where the right half the graph starts at -pi/2
Do you even know how this cardioid look like? Take a peek here:
File:CardioidsLabeled.PNG - Wikipedia, the free encyclopedia
Your cardioid is the green one, and then you can see why the area wanted can be divided when the angle is taken from Pi/6 to -pi/2 and multipled by two (it is symmetric with respect to the y-axis)
Tonio
Yes, but you have to go from below! Looking at the picture one sees that you better integrate from, to force the path to "run" below the x-axis (most of the time),
If you do as you say the path will go above the x-axis and you'll be evaluating something wrong.
Tonio
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