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Mathematics

Mathematics. Session. Definite Integrals - 3. Session Objectives. Definite Integral as the Limit of a Sum Areas of Bounded Regions Class Exercise. Definite Integral as the Limit of a Sum. OR. Example - 1. Solution Cont. Example - 2. Solution Cont. Example - 3. Solution Cont.

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Mathematics

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  1. Mathematics

  2. Session Definite Integrals - 3

  3. Session Objectives • Definite Integral as the Limit of a Sum • Areas of Bounded Regions • Class Exercise

  4. Definite Integral as the Limit of a Sum OR

  5. Example - 1

  6. Solution Cont.

  7. Example - 2

  8. Solution Cont.

  9. Example - 3

  10. Solution Cont.

  11. Example - 4

  12. Solution Cont.

  13. Example - 5

  14. Solution Cont.

  15. Areas of Bounded Regions 1. Let f(x) be a continuous function defined on the interval [a, b]. Then, the area bounded by the curve y = f(x), x-axis and the ordinates x = a, x = b is • The area bounded by the curve x = f(y), y-axis and the abscissae y = c, y = d is

  16. Areas of Bounded Regions Cont.

  17. Example - 6

  18. Solution Cont.

  19. Example - 7

  20. Solution Cont.

  21. Solution Cont.

  22. Example - 8 Solution: The given curves are (i) and (ii) intersect at (1, 0) and (0, 1).

  23. Solution Cont.

  24. Example - 9

  25. Solution Cont.

  26. Example - 10 Solution: The given curves are

  27. Solution Cont.

  28. Solution Cont.

  29. Solution Cont.

  30. Example - 11

  31. y x2 + y2 = 1 x x' (1, 0) O (x-1)2 + y2 = 1 y' Solution Cont.

  32. Solution Cont.

  33. Solution Cont.

  34. Thank you

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