The boundaries of doule integrals in polar form

In summary, the boundaries of a double integral in polar form are determined by the limits of the radial coordinate (r) and the angular coordinate (θ). To convert Cartesian coordinates (x, y) to polar coordinates (r, θ), use the equations r = √(x^2 + y^2) and θ = arctan(y/x). The Jacobian in polar coordinates is used to convert the double integral from Cartesian form to polar form and accounts for the change in area when switching from rectangular to polar coordinates. The boundaries of a double integral in polar form can be negative, as polar coordinates can have negative values for both r and θ. The limits of integration for a double integral in polar form are determined
  • #1
winbacker
13
0
Hi I need to use a double integral to find the area of the region bounded by:

r = 3 + 3sinQ where Q = theta.

I know the bounds of the inner integral are from 0 to 3 + 3sinQ.

However, I do not know how to determine the bounds of the outer integral.

Any help would be greatly appreciated.
 
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  • #2
Ok this seems to be a cardioid. What you found were the boundaries of r. So Where is the problem of finding theta? Just graph it. If all else fails plug in some values of theta.
 

What are the boundaries of a double integral in polar form?

The boundaries of a double integral in polar form are determined by the limits of the radial coordinate (r) and the angular coordinate (θ).

How do I convert Cartesian coordinates to polar coordinates?

To convert Cartesian coordinates (x, y) to polar coordinates (r, θ), use the following equations:
r = √(x^2 + y^2)
θ = arctan(y/x)

What is the significance of the Jacobian in polar coordinates?

The Jacobian in polar coordinates is used to convert the double integral from Cartesian form to polar form. It accounts for the change in area when switching from rectangular to polar coordinates.

Can the boundaries of a double integral in polar form be negative?

Yes, the boundaries of a double integral in polar form can be negative. This is because polar coordinates can have negative values for both r and θ.

How do I determine the limits of integration for a double integral in polar form?

The limits of integration for a double integral in polar form are determined by the region of integration. This region can be defined by the inequalities of r and θ or by a graph of the region.

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