WHY DO WE NEED INTEGRATION?

Why do we need integration?

In physics, integration crops up pretty much everywhere. Work is the integral of force over a distance, for example. Electric flux is an integral of the electric field over a surface. In other sciences, you might want to compute the area under a curve. (Don’t re-invent calculus like this though). In pure math, integrals are used for concepts such as winding numbers and are irreplaceable for results such as the general Stokes’ theorem.

However based on that embedded question, is it worth just focusing on differentiation and move on to multi-variable differentiation instead of spending more time on integration?

No.

Do we have integrals in multi variable calculus? Is there any practical use of integration?

Absolutely. See multiple integralline integralsurface integralcontour integral (admittedly, a particular type of line integral, but it holds special importance).

What is the most important prerequisite for Stochastic calculus?

Calculus and probability theory (not statistics!)


By the way, is this question motivated by how difficult it is to do integrals vs. the relative easiness of finding derivatives?

Source:  Henry Swanson

Is it worth just focusing on differentiation and move on to multi-variable differentiation instead of spending more time on integration?

No, you should learn how to integrate before moving onto multivariate calculus.

Do we have integrals in multi variable calculus?

Yes, http://en.wikipedia.org/wiki/Multiple_integral

Is there any practical use of integration?

Yes. Engineering, physics (for example electric field), almost everything scientific uses integration.

What is the most important prerequisite for Stochastic calculus?

Calculus