DinS Written on 2018/4/24

Anti-differentiation is a bridge between differentiation and integration

1. What’s anti-differentiation?

We have now covered differentiation. What if we work our way the opposite direction?

For example, f(x) = x². F’(x) = 2x. Now if we take f(x) as a derivative of some other function, say g’(x) = f(x), what’s g(x)?

This is an easy case, and we can get . Wait a second, what about ?

So you see, this process is anti-differentiating, and we can get many anti- derivatives. The difference is the constant term.

If F is an anti-derivative of f, we’ll write:

Just some fancy notations. You’ll get used to it. Here’re some rules to anti-derivative.

See an example of anti-differentiation.

I hope this isn’t too bad. Surely it feels harder than differentiation. And things can get really crazy if you try some harder example, say ∫ logxdx.

Sometimes it’s impossible to find anti-differentiation. This feels the same for multiply and factoring. It’s easy to multiply; it’s hard to factor.

What’s the meaning of anti-differentiation? It will shine when we reach the part of integration. Right now see it as a mind-quiz.