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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
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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
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
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
THE FUNDAMENTAL THEOREM OF CALCULUS THE FUNDAMENTAL THEOREM OF CALCULUS, PART 2 Example: Evaluate the integral
THE FUNDAMENTAL THEOREM OF CALCULUS Define: Example: Example:
THE FUNDAMENTAL THEOREM OF CALCULUS THE FUNDAMENTAL THEOREM OF CALCULUS, PART 1 Example: Find the derivative of the function Note: Using Leibniz notation
THE FUNDAMENTAL THEOREM OF CALCULUS THE FUNDAMENTAL THEOREM OF CALCULUS, PART 1 Note: Using Leibniz notation Example: Find
THE FUNDAMENTAL THEOREM OF CALCULUS THE FUNDAMENTAL THEOREM OF CALCULUS, PART 1 Note: Using Leibniz notation Example: Find Note:
THE FUNDAMENTAL THEOREM OF CALCULUS Note: Note: Note:
THE FUNDAMENTAL THEOREM OF CALCULUS Note 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
Total Area Example Evaluate:
Total Area Example Find the area of the region between the x-axis and the graph of Example Find the area of the region between the x-axis and the graph of What is the difference between these two examples