Basics
of Multiple Integrals and Applications
(continued)
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Here the first integration is on the y-variable. You can picture this as “sweeping” the element of area from y1 to y2 followed by “sweeping” the rectangle from x1a to x2a . The same strategy (but more complicated) applies for calculating volumes between two intersecting surfaces. In this case the element of volume is dV = dx dy dz if you "sweep" the volume first in x, then in y, and finally in z directions. Click here for two examples involving double integrals. |
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