The Fundamental Theorem of Calculus (Part 2)
FTC 2 relates a definite
integral of a function to the net change in its antiderivative.
Fundamental
Theorem of Calculus (Part 2): If f is
continuous on [a,b], and F′(x)=f(x), then ∫baf(x)dx=F(b)−F(a).
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This FTC 2 can be written in
a way that clearly shows the derivative and antiderivative
relationship, as
∫bag′(x)dx=g(b)−g(a).
This gives us an incredibly powerful way
to compute definite integrals:
- Find an antiderivative.
- Evaluate it at the limits of integration.
This computation is the most important use of FTC
2 in this course.
Example: DO:
use the FTC to evaluate ∫313x2dx.
The following video gives examples of using FTC
2 to evaluate definite integrals.
The following video explains FTC 2.
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