line integrals

OK, so the main thing to know about this exam is how to set up and evaluate double integrals and line integrals.

Line integrals are used extensively in the theory of functions of a complex variable.

What if I add all of the small line integrals?

So, the fundamental theorem of calculus, not for line integrals, tells you if you integrate a derivative, then you get back the function.

I mean, basically starting at the end of next week, we are going to do triple integrals, line integrals in space and so on.

It is not a surprise that you will get the same answer for both line integrals.

OK, so this doesn't tell us what each of these two line integrals is.

Some of them compute different line integrals.

Reducing line integrals to ordinary integrals.

Unfortunately, it is not quite as simple as with line integrals.

You have three line integrals to compute instead of two, but conceptually it remains exactly the same idea.

Let's start right away with line integrals in space.

We've learned about double integrals, and we've learned about line integrals.

OK, so that should give you overview of various ways to compute line integrals.

So, we've also seen about line integrals.

So conceptually it is very similar to line integrals.

So, these are special cases of what's called the fundamental theorem of calculus for line integrals.

So, line integrals we know how to evaluate.

So, Green's theorem is another way to avoid calculating line integrals if we don't want to.

OK, so I proved that my two line integrals along C1 and C2 are equal.

Supplement of the Relations Between Two Curve Line Integrals

Double integrals and line integrals in the plane;

line integrals of the first type

line integrals of the second type