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)#