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Single Variable Calculus
3. The Definite Integral and its Applications
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The derivative tells us the rate of change of a function whose values we know. The definite integral tells us the value of a function whose rate of change and initial conditions are known.
Part A: Definition of the Definite Integral and First Fundamental Theorem
Part B: Second Fundamental Theorem, Areas, Volumes
Part C: Average Value, Probability and Numerical Integration
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Massachusetts Institute of Technology