Evaluate the double integral [math] where [math] is the top half of the disc with center the origin and radius [math] by changing to polar coordinates.
Answer:
Convert the integral [math] to polar coordinates and evaluate it (use [math] for [math]):
With [math] , [math] , [math] and [math] ,
[math] [math]
[math] [math]
[math] .
Sketch the region of integration for the following integral.
[math]
The region of integration is bounded by
Consider the solid shaped like an ice cream cone that is bounded by the functions [math] and [math] Set up an integral in polar coordinates to find the volume of this ice cream cone.
Instructions: Please enter the integrand in the first answer box, typing theta for [math]. Depending on the order of integration you choose, enter dr and dtheta in either order into the second and third answer boxes with only one dr or dtheta in each box. Then, enter the limits of integration and evaluate the integral to find the volume.
[math]
A =
B =
C =
D =
Volume =
Note: You can earn partial credit on this problem.
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