Antiderivatives: True/False Exercises

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Here we’ll practice T/F with antiderivatives.

If $f$ and $g$ both have the same antiderivative, then $f = g$

True False

Let $F$ be an antiderivative of $f$ , and $G$ be an antiderivative of $g$ . If $f(x)$ is always less than $g(x)$ , then $F(x)$ is always less than $G(x)$

True False

Let $F$ be an antiderivative of $f$ . If $f$ is increasing on an interval, then $F$ must be positive on that interval.

True False

Let $F$ and $G$ be antiderivatives of $f$ , which is continuous on the whole real line. Then $F(1)-F(0) = G(1)-G(0)$

True False

If $f'(x) = x^2$ , then $f$ is an antiderivative of $x^2$ .

True False

The antiderivative of a constant function is a linear function.

True False

If $F$ is an antiderivative of $f$ , which is defined on the whole real line, then $F$ is continuous.

True False