
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
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 bottomleft quadrant of the circle described by : And the square is just the area bound between the line y(x) and the xaxis 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<x<R. Then the centroid coordinates are: The substitution is elementary, but sufficed to say, . Also, we have: And it is shown the centroid is . 
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 
Search tags for this page 
square minus circle centroid,how to find centroid quarter circle,quarter circle centroid,centroid of a square minus a circle,quarter circle formulae,centroid of quadrant of circle by integration,centroid of a quarter circle,centroid of a square minus a quarter circle,centroid squarer minus quarter circle,how to find centroid of circle &half circle
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Equation detecting overlapping square and circle.  Abomb1126  Computer Science  3  December 11th, 2013 12:01 PM 
Polar math problem regarding tangents to a polar curve  sanchay09  Calculus  5  October 10th, 2013 12:21 AM 
Maximum Area of Circle and Square  zerostalk  Algebra  6  January 10th, 2012 08:06 PM 
Any conformal map from square to unit circle?  lumiere137  Complex Analysis  0  October 19th, 2010 05:00 AM 
Polar math problem regarding tangents to a polar curve  sanchay09  Algebra  1  December 31st, 1969 04:00 PM 