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If the derivative of a constant is $0$ then what is the integral of a constant?

What is the integral of $0$?

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2 Answers

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Remember that the fundamental theorem of calculus says (essentially)

if $F$ is an antiderivative of $f$ (i.e. $F' = f$), then $\int f = F + C$.

So, answer your own questions:

1) What kinds of functions have constants as their derivatives (i.e. given $f = $constant, what could $F$ be?)

2) What kinds of functions have $0$ as their derivatives (i.e. given $f = 0$, what could $F$ be?)

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The integral of a constant $C$ with respect to $x$ is $Cx + A$, $A$ constant. Applying this rule to the constant function $y(x) = 0$, $\int {0}dx = 0+A = A$.

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