What is the antiderivative of a constant?

1 Answer
Dec 31, 2015

I find it simpler to think of this looking at the derivative first.

Explanation:

I mean: what, after being differentiated, would result in a constant? Of course, a first degree variable.

For example, if your differentiation resulted in f'(x)=5, it's evident that the antiderivative is F(x)=5x

So, the antiderivative of a constant is it times the variable in question (be it x, y, etc.)

We could put it this way, mathematically:

intcdx <=> cx

Note that c is mutiplying 1 in the integral:

intcolor(green)(1)*cdx <=> cx

That means first degree variable being differentiated:

f(x)=x^color(green)(1), then f'(x)=color(green)1*x^(1-1)=1*x^0=color(green)(1)