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Mastering Definite Integrals: Fundamental Theorem and Substitution

Learn how to evaluate definite integrals using the Fundamental Theorem of Integral Calculus and substitution. Practice with examples and improve your skills in handling integrals on specific intervals.

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Mastering Definite Integrals: Fundamental Theorem and Substitution

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Presentation Transcript

  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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