Advanced Placement Calculus AB covering limits, derivatives, and integrals.
The Fundamental Theorem of Calculus links differentiation and integration—it’s the bridge that connects the two main ideas of calculus.
If \( F \) is an antiderivative of \( f \), then:
\[ \int_{a}^{b} f(x) , dx = F(b) - F(a) \]
This means you can compute definite integrals using antiderivatives!
You can calculate areas, solve accumulation problems, and connect the ideas of rates and totals—all with one powerful theorem.
\[\int_{a}^{b} f(x) , dx = F(b) - F(a)\]
Find the area under \( f(x) = 2x \) from \( x = 1 \) to \( x = 4 \) using the Fundamental Theorem.
Calculate the total distance traveled using the velocity function over a time interval.
The Fundamental Theorem connects derivatives and integrals, making calculating areas and totals much easier.