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THE FUNDAMENTAL THEOREM OF CALCULUS

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

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  1. 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

  2. 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

  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

  4. THE FUNDAMENTAL THEOREM OF CALCULUS THE FUNDAMENTAL THEOREM OF CALCULUS, PART 2 Example: Evaluate the integral

  5. THE FUNDAMENTAL THEOREM OF CALCULUS Define: Example: Example:

  6. THE FUNDAMENTAL THEOREM OF CALCULUS THE FUNDAMENTAL THEOREM OF CALCULUS, PART 1 Example: Find the derivative of the function Note: Using Leibniz notation

  7. THE FUNDAMENTAL THEOREM OF CALCULUS THE FUNDAMENTAL THEOREM OF CALCULUS, PART 1 Note: Using Leibniz notation Example: Find

  8. THE FUNDAMENTAL THEOREM OF CALCULUS THE FUNDAMENTAL THEOREM OF CALCULUS, PART 1 Note: Using Leibniz notation Example: Find Note:

  9. THE FUNDAMENTAL THEOREM OF CALCULUS Note: Note: Note:

  10. 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

  11. Total Area Example Evaluate:

  12. Total Area

  13. 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

  14. TERM-102

  15. TERM-102

  16. TERM-092

  17. TERM-082

  18. TERM-082

  19. TERM-082

  20. TERM-091

  21. TERM-093

  22. TERM-091

  23. Term-092

  24. Term-082

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