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 June 13th, 2013, 04:27 PM #1 Member   Joined: Dec 2010 Posts: 51 Thanks: 0 Polar function from a (circle and square) shape http://i.imgur.com/sUM8fwH.gif I'm trying to find the area of the blue shape (technically i'm trying to find the centroid). How would i setup the integral in polar form? June 13th, 2013, 06:50 PM #2 Senior Member   Joined: Jan 2013 Posts: 113 Thanks: 0 Re: Polar function from a (circle and square) shape If the image is accurate, so that the the axes are at a tangent to the circle, then an integral is not really necessary. We have a quarter circle and a square. Hence the area shown is If you want to do it with integration, just do the same thing. Consider the graph illustrating the two functions: Then, being explicit with your request, we can find the area of the bottom-left quadrant of the circle described by : And the square is just the area bound between the line y(x) and the x-axis from -R to 0. Notice that since the line is below the axis, we're going to get the negative area. To correct, we'll just multiply by -1: And then the area of the blue is the square minus the quarter circle: To find the centroid of an object with upper bound f(x) and lower bound g(x) over the region , the following formulae can be applied to find the centroid : Where A is the area of the shape enclosed by f and g. Formulae thanks to wiki. If we let: And Then it's clear the area enclosed is , since f and g are two halves of a circle with radius R. We will look at the region -R
 June 14th, 2013, 02:00 PM #3 Member   Joined: Dec 2010 Posts: 51 Thanks: 0 Re: Polar function from a (circle and square) shape thank you very much  Tags circle, function, polar, shape, square ,

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how to find centroid of circle &half circle

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