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The Fundamental Theorem of Calculus is appropriately named because it establishes connection between the two branches of calculus: differential calculus and integral calculus. THE FUNDAMENTAL THEOREM OF CALCULUS Let: Find the an antiderivative Example A function is called an antiderivative of if DEFINITION
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Example: THE FUNDAMENTAL THEOREM OF CALCULUS, PART 2 THE FUNDAMENTAL THEOREM OF CALCULUS Evaluate the integral Example: Find the area under the curve from x-0 to x=1
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Example: THE FUNDAMENTAL THEOREM OF CALCULUS, PART 2 THE FUNDAMENTAL THEOREM OF CALCULUS Evaluate the integral Example: Find the area under the curve from x-0 to
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Example: THE FUNDAMENTAL THEOREM OF CALCULUS, PART 2 THE FUNDAMENTAL THEOREM OF CALCULUS Evaluate the integral
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Define: Example: THE FUNDAMENTAL THEOREM OF CALCULUS Example:
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THE FUNDAMENTAL THEOREM OF CALCULUS, PART 1 THE FUNDAMENTAL THEOREM OF CALCULUS Find the derivative of the function Note: Using Leibniz notation
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Example: THE FUNDAMENTAL THEOREM OF CALCULUS Find THE FUNDAMENTAL THEOREM OF CALCULUS, PART 1 Note: Using Leibniz notation
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THE FUNDAMENTAL THEOREM OF CALCULUS THE FUNDAMENTAL THEOREM OF CALCULUS, PART 1 Note: Using Leibniz notation Example: Find Note:
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THE FUNDAMENTAL THEOREM OF CALCULUS Note:
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Note 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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Total Area Example Evaluate:
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Total Area
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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
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TERM-102
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TERM-092
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TERM-082
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TERM-091
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TERM-093
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TERM-091
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Term-092
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Term-082
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