Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS The Fundamental Theorem of Calculus is appropriately named because it establishes connection between the two branches of calculus: differential calculus and integral calculus. DEFINITION Example A function is called an antiderivative of if Let: Find the an antiderivative
Example: Example: Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS THE FUNDAMENTAL THEOREM OF CALCULUS, PART 2 Example: Evaluate the integral Example: Find the area under the curve from x-0 to x=1
Example: Example: Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS THE FUNDAMENTAL THEOREM OF CALCULUS, PART 2 Example: Evaluate the integral Example: Find the area under the curve from x-0 to
Example: Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS THE FUNDAMENTAL THEOREM OF CALCULUS, PART 2 Example: Evaluate the integral
Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS Define: Example: Example:
Example: Note: Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS THE FUNDAMENTAL THEOREM OF CALCULUS, PART 1 Example: Find the derivative of the function Note: Using Leibniz notation
Note: Example: Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS THE FUNDAMENTAL THEOREM OF CALCULUS, PART 1 Note: Using Leibniz notation Example: Find
Note: Example: Note: Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS THE FUNDAMENTAL THEOREM OF CALCULUS, PART 1 Note: Using Leibniz notation Example: Find Note:
Note: Example: Note: Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS THE FUNDAMENTAL THEOREM OF CALCULUS, PART 1 Note: Using Leibniz notation Example: Find Note:
Note: Note: Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS THE FUNDAMENTAL THEOREM OF CALCULUS, PART 1 Note: Using Leibniz notation Note:
Note Note Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS which says that if f is integrated and then the result is differentiated, we arrive back at the original function Note This version says that if we take a function , first differentiate it, and then integrate the result, we arrive back at the original function
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