Question

Can someone explain what a surface integral in geometric terms? How is it different from a normal double integral? E.g. a single integral is the area between the curve and the x-axis.

Answer 1

It is akin to the length of a function with one integral :\[\int\limits_{0}^{k} \sqrt{1+(dy/dx)^2} dx\]. The double is the area under a curve. The surface integral is a 3D arc-length.

Answer 2

Thank you for posting a Calc question.

Answer 3

Wait, isnt arc length for line integrals?

Answer 4

Yes, I'm suggesting an analogy. Hat is to head as lampshade is to lamp. Arc-length is to 2-D graphs as surface integrals are to 3D.

Answer 5

The line integral is the area under the 3d curve and the xy plane, where height is given by z = f(x,y). I mam looking for a similar explanation for the surface integral.

Answer 6

The line integral is the area under the 3d curve and the xy plane, where height is given by z = f(x,y). I mam looking for a similar explanation for the surface integral.

Answer 7

The surface integral is "the double integral analog of the line integral"

Answer 8

Then, thats the same as the double integral - area under a surface? Thx for ur help btw.

Answer 9

Both double and surface integral gives the volume right?

Answer 10

When you take a double integral, you only input the function. With a surface integral you put in the partial derivatives of a function. \[\int\limits_{a}^{b}\int\limits_{c}^{d}\sqrt{(\delta f/ \delta x)^2 +(\delta f/ \delta y)^2 +1 } dx dy\]

Answer 11

This is the surface integral for the surface area of a function.

Answer 12

Thanks I kind of get it now.