The Evaluation Theorem states that the integral of a continuous function over an interval can be found using its antiderivative. Specifically, if $F$ is an antiderivative of $f$, then $\int_a^b f(x) \, dx = F(b) - F(a)$.
5 Must Know Facts For Your Next Test
The Evaluation Theorem is a direct consequence of the Fundamental Theorem of Calculus.
It requires finding an antiderivative $F$ such that $F'(x) = f(x)$.
The theorem simplifies the process of calculating definite integrals.
Both the lower limit $a$ and the upper limit $b$ are essential in evaluating the integral.
The notation $\int_a^b f(x) \, dx$ represents the area under the curve from $x=a$ to $x=b$.
Review Questions
Related terms
Definite Integral: The definite integral of a function over an interval [a,b] gives the net area under its curve between those points.
Antiderivative: An antiderivative of a function \( f \) is another function \( F \) such that \( F' = f \).