The Fundamental Theorem of Calculus is appropriately named because it establishes connection between the two branches of calculus: differential calculus and integral calculus. Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS Let: Find the an antiderivative Example A function is called an antiderivative of if DEFINITION

Example: THE FUNDAMENTAL THEOREM OF CALCULUS, PART 2 Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS Evaluate the integral Example: Find the area under the curve from x-0 to x=1

Example: THE FUNDAMENTAL THEOREM OF CALCULUS, PART 2 Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS Evaluate the integral Example: Find the area under the curve from x-0 to

Example: THE FUNDAMENTAL THEOREM OF CALCULUS, PART 2 Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS Evaluate the integral

Define: Example: Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS Example:

THE FUNDAMENTAL THEOREM OF CALCULUS, PART 1 Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS Find the derivative of the function Note: Using Leibniz notation

Example: THE FUNDAMENTAL THEOREM OF CALCULUS, PART 1 Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS Find Note: Using Leibniz notation

Example: THE FUNDAMENTAL THEOREM OF CALCULUS, PART 1 Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS Find Note: Using Leibniz notation Note:

Example: THE FUNDAMENTAL THEOREM OF CALCULUS, PART 1 Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS Find Note: Using Leibniz notation Note:

THE FUNDAMENTAL THEOREM OF CALCULUS, PART 1 Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS Note: Using Leibniz notation 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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