6.7 The Fundamental Theorem of Calculus and Definite Integrals
- Syllabus
- 2020
- Topic
- 6.7
- Level
- —
FUN-6.B—Evaluate definite integrals analytically using the Fundamental Theorem of Calculus
- FUN-6.B Evaluate definite integrals analytically using the Fundamental Theorem of Calculus.
- FUN-6.B.1 An antiderivative of a function f is a function g whose derivative is f.
- FUN-6.B.2 If a function f is continuous on an interval containing a, the function defined by F(x) = ∫ₐˣ f(t)dt is an antiderivative of f for x in the interval.
- FUN-6.B.3 If f is continuous on the interval [a, b] and F is an antiderivative of f, then ∫ₐᵇ f(x)dx = F(b) − F(a).
- Enduring understanding FUN-6: Recognizing opportunities to apply knowledge of geometry and mathematical rules can simplify integration.
Objective notes
1 learning objectiveConceptAP Calculus BC