How line integral generalizes definite integral?

A line integral is a simple integral. they look like: integral x=a to b of (f(x)). A surface integral is an integral of two variables. they look like: integral x=a to b, y=c to d of (f(x,y)). or...

By using the fundamental theorem of Calculus. i.e. The integral of f(x) = F(x), your limits are [a,b]. Solve: F(b) - F(a). The FTC, second part, says that if f is a continuous real valued function...

It tells you the area of the function (curve) between the two limits.

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You'll want to understand the different techniques for different types of integrals. For instance, simple polynomials can be integrated very easily, whereas a product of functions has a special...