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Double integral using polar coordinates
- Thread starter Miike012
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In summary, the conversation discusses the use of polar and spherical coordinates in integration. The question is asked about why 0 to pi is integrated instead of 0 to 2pi, and it is determined that it depends on the region on the xy plane. The conversation also touches on when to use cylindrical or rectangular coordinates for different shapes.
- #2
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Miike012 said:
Draw a picture of the region.
- #3
- #4
Miike012
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Sorry I just looked at the question again.. it said above the x-axis
- #5
- 9,568
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So does that answer your question?
- #6
Miike012
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One last question. When is it best to use polar coordinates rather than spher. coord. For instance if I integrating a cylinder I would use polar and If I was integrating a cone or a ellipsoid I should use spher. coord. But what about elliptical parabaloids or eliptic hyperbolas of one or two sheets?
- #7
Miike012
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To answer my above question (post # 6) I am guessing is depends on my region on the xy plane that I am integrating over..
- #8
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Miike012 said:
You have the right general division of the methods. Sometimes they overlap though. A paraboloid would suggest cylindrical coordinates for the elliptical cross section but rectangular if you were doing one of the other cross sections. Similarly for the hyperboloids.
Related to Double integral using polar coordinates
What is a double integral using polar coordinates?
A double integral using polar coordinates is a mathematical technique for calculating the area under a curve on a polar graph. It involves converting the cartesian coordinates (x, y) into polar coordinates (r, θ) and then integrating with respect to r and θ.
Why use polar coordinates for a double integral?
Polar coordinates are useful for calculating the area under curves that have circular or symmetrical shapes. They can also simplify certain integrals and make them easier to solve.
How do you set up a double integral using polar coordinates?
To set up a double integral using polar coordinates, you first need to convert the limits of integration from cartesian to polar coordinates. Then, you need to multiply the function by the Jacobian, which is the determinant of the transformation matrix. Finally, you integrate with respect to r and θ using the appropriate limits.
What is the difference between a single and double integral using polar coordinates?
A single integral using polar coordinates calculates the area under a curve in a polar graph, while a double integral calculates the volume under a surface in a polar graph. The single integral has one variable (r), while the double integral has two variables (r and θ).
What are some applications of double integrals using polar coordinates?
Double integrals using polar coordinates are used in many fields of science and engineering, such as physics, engineering, and astronomy. They are particularly useful for calculating the moments of inertia of objects with circular or symmetrical shapes.
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