Double Integrals

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by stephaniejoy19
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Double Integrals

Double Integrals

Double Integrals give the volume under a surface over a 2-dimensional region in the x-y plane.

Sometimes, we aren't lucky enough to have a rectangular region to work with, though...

Here's how to solve the most basic type - the volume over a rectangular region.

Sometimes, it becomes significantly easier to solve a double integral if we can convert it from Cartesian to Polar Coordinates. See an example of how to do this here!

In addition to changing the integral from Cartesian to Polar, sometimes it is necessary to change the order of integration.When we are dealing with a rectangular region, changing the order of integration is as simple as switching the inner and outer bounds, and changing dydx to dxdy (or vice-versa).However, if we are dealing with a more general region, it is not quite that simple.

See the general procedure for changing the order of integration in the video to the right! -->


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