Converting Cartesian to Polar Coordinates for a Double Integral

In summary, the conversation discusses how to convert a double integral from cartesian coordinates to polar coordinates. The integral in cartesian coordinates has a troublesome minus sign, and the individual is unsure how to convert the region into polar coordinates. They ask for clarification and eventually figure out that y = rsintheta in polar coordinates.
  • #1
CaptainEvil
99
0
I'm working on a double integral and need to change from cartesian to polar coords.

The double integral in cartesian coords is
Double integral from 0 to a (in dy) and from -sqrt(a^2 - y^2) in dx (NOTE minus sign before sqrt)

the little minus sign is troubling. How would I convert this region into polar coords?
 
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  • #2
I'm guessing your a is your radius? So what does y = ?
 
  • #3
the whole question is

Double integral
(0 to a) (-sqrt(a^2 - y^2) to 0) of x^2y dxdy
 
  • #4
Right, I'm asking you in polar coordinates, what does y =?
 
  • #5
y = rsintheta

but I solved it, thanks anyway
 
  • #6
Doesn't it equal a sin(theta) here?
 

1. What is the purpose of changing to polar coordinates?

Changing to polar coordinates is often used in mathematics and physics to simplify complex problems involving circular or spherical shapes. It can also make certain calculations, such as finding the distance between two points, easier to solve.

2. How do I convert from Cartesian coordinates to polar coordinates?

To convert from Cartesian coordinates (x,y) to polar coordinates (r,θ), you can use the following formulas: r = √(x² + y²) and θ = arctan(y/x). Alternatively, there are online calculators and software programs that can do the conversion for you.

3. Can polar coordinates be negative?

Yes, polar coordinates can be negative. The radius (r) can be negative if the point is in the third or fourth quadrant, and the angle (θ) can be negative if the point is in the second or third quadrant.

4. What is the difference between polar and cylindrical coordinates?

While both polar and cylindrical coordinates use a radius (r) and an angle (θ) to represent a point, cylindrical coordinates also include a height (z) value to represent the distance along the z-axis. This is often used in 3D problems involving cylindrical shapes.

5. How can I graph polar coordinates?

Graphing polar coordinates is similar to graphing Cartesian coordinates, but instead of using x and y axes, you will use a polar grid with a radius and angle axis. To plot a point, you would find the corresponding radius and angle values and mark it on the grid. Online graphing tools or software programs can also help with visualizing polar coordinates.

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