Move polygon ABCD to a location of your choice on the coordinate plane, and change the orientation of . Be sure that the preimag
e ABCD does not overlap the image AEFBEFCEFDEF when you're through. Next, find the perpendicular distance between each vertex of ABCD and . Enter the values in the table. Do the same for the perpendicular distance between each vertex of the reflected shape AEFBEFCEFDEF and . Record all of your answers to one decimal place.
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The value of the given surface integral is 4.
The given plane intercepts the coordinate axes at (2, 0, 0), (0, 2, 0), and (4, 0, 0). These point are the coordinates of a triangular region that we can parameterize using.
A surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analog of the line integral. Given a surface, one may integrate a scalar field over the surface or a vector field.
with 0≤u≤1 and 0≤v≤1. Then the surface element ds is equivalent to
The surface integral is then
Therefore the value of the given surface integral is 4.
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