Question

What is the antiderivative of a constant?

Answer 1

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)`