What are the limits for a double polar integral in the first quadrant?

In summary, the conversation is about a double integral problem with limits of infinity and the need to convert it into polar form and evaluate it. The person asking for help is unsure how to convert the limits to polar coordinates and is struggling with understanding how to sketch the integration area in polar coordinates. The expert responding is surprised that the instructor did not provide any guidance on polar coordinates and suggests looking for information on the "differential of area" in polar coordinates in the textbook. They also clarify that the limits of infinity mean that x and y can take on all non-negative values in the first quadrant and prompt the person to think about what r and θ range over in the first quadrant.
  • #1
BananaMan
41
0
i have the integral [tex]\int_{0}^{\infty} \int_{0}^{\infty} (-x^2-y^2) \ dx dy[/tex]
(double integral with both limits the same...assuming my first bash at the tex comes out

it says to transfer it into polar form and evaluate it

i have no idea how to convert a limit of infinity to polar form, help please
 
Last edited:
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  • #2
Really? Your instructor has given you this problem without the slightest indication of what polar coordinates are? What an evil person! And you textbook doesn't have anything about the "differential of area" in polar coordinates?? Are you sure you are reading it correctly?
 
  • #3
no, we have gone over polar co-ordinates, but never with an integration limit of infinity so i have no idea how to convert the limit to evaluate it
 
  • #4
Make a skech of the integration area for x and y.
How can you cover the same area in polar coördinates?
 
  • #5
how do you sketch the area of x or y to infinity though?
 
  • #6
Are you serious? x going from 0 to [itex]\infty[/tex] and y going from 0 to [itex]\infty[/itex] means that x and y may take on all non-negative values- the first quadrant. Now, what do r and [itex]\theta[/itex] range over in the first quadrant?
 

What is a double integral in polar form?

A double integral in polar form is a mathematical operation used to calculate the area of a region in a polar coordinate system. It involves integrating a function over a region bounded by two polar curves.

How is a double integral in polar form different from a regular double integral?

A double integral in polar form is different from a regular double integral because it uses a polar coordinate system instead of rectangular coordinates. This allows for easier integration when dealing with circular or symmetrical regions.

What is the formula for a double integral in polar form?

The formula for a double integral in polar form is ∫∫R f(r,θ) r dr dθ, where R is the region of integration, f(r,θ) is the integrand, r is the radial distance, and θ is the angle.

What are some real-world applications of double integrals in polar form?

Double integrals in polar form are used in a variety of fields, such as physics, engineering, and economics. Some real-world applications include calculating the moment of inertia of a rotating object, finding the center of mass of a symmetrical object, and determining the volume of a solid with a curved base.

What are some common mistakes when solving a double integral in polar form?

Some common mistakes when solving a double integral in polar form include forgetting to include the correct conversion factor r when switching from rectangular to polar coordinates, integrating with respect to the wrong variable, and not properly setting up the limits of integration for the region.

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