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Mathematics

Mathematics. Session. Definite Integrals –1. Session Objectives. Fundamental Theorem of Integral Calculus Evaluation of Definite Integrals by Substitution Class Exercise. Fundamental Theorem of Integral Calculus.

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Mathematics

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  1. Mathematics

  2. Session Definite Integrals –1

  3. Session Objectives • Fundamental Theorem of Integral Calculus • Evaluation of Definite Integrals by Substitution • Class Exercise

  4. Fundamental Theorem of Integral Calculus Let F(x) be any primitive (or antiderivative) of a continuous function f(x) defined on an interval [a, b]. Then the definite integral of f(x) over the interval [a, b] is given by ‘a’ is called the lower limit and ‘b’ the upper limit. Note: The value of a definite integral is unique.

  5. Example - 1

  6. Example - 2

  7. Solution Cont.

  8. Example - 3

  9. Solution Cont.

  10. Example - 4

  11. Example - 5

  12. Solution Cont.

  13. Example - 6

  14. Evaluation of Definite Integrals by Substitution Now find the result using the fundamental theorem.

  15. Example - 7

  16. Example - 8

  17. Solution Cont.

  18. Example - 9

  19. Solution Cont.

  20. Example - 10

  21. Solution Cont.

  22. Example - 11

  23. Solution Cont.

  24. Solution Cont.

  25. Thank you

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