We began today's lesson with a simple set up of an integral to find surface area. As we quickly learned, sometimes we can use polar to make bounds easier to define, or make an integral much easier to solve. We then moved on to surface integrals. Surface integrals are evaluated just like line integrals, with the exception of a double integral instead of a single one.
Here it is in single integral form:
Here it is in single integral form:
Simply account for the second integral, and you are set to begin solving surface integrals!
The homework for today is to do page 1122 # 2, 5, 14, 18 and 22. In addition if you have not yet done so, don't forget to do the utexas on parametric surfaces which is due TONIGHT!!
ReplyDeleteInterestingly, the formula to find surface area is very similar to the arc length formula. Just like how the line integral formula is similar to the formula to find mass, the double line integral formula can be adjusted and become the formula to find surface area!
ReplyDeleteIt may not be the most useful technique, but it's cool how you can change the region (where you're finding the surface area) that's usually looked as a region on the xy plane and instead look at it as a region on the yz plane.
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