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AP Calculus BC Friday, 07 March 2014

AP Calculus BC Friday, 07 March 2014. OBJECTIVE TSW (1) evaluate an improper integral that has an infinite limit of integration, and (2) evaluate an improper integral that has an infinite discontinuity. ASSIGNMENTS DUE TODAY NOTHING!!! ASSIGNMENTS DUE MONDAY WS The Logistics Curve

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AP Calculus BC Friday, 07 March 2014

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  1. AP Calculus BCFriday, 07 March 2014 • OBJECTIVETSW (1) evaluate an improper integral that has an infinite limit of integration, and (2) evaluate an improper integral that has an infinite discontinuity. • ASSIGNMENTS DUE TODAY • NOTHING!!! • ASSIGNMENTS DUE MONDAY • WS The Logistics Curve • Sec. 8.7: p. 574 (11-35 odd, 37-51 odd omit part C) • REMINDER • PI Day: Next Friday, 14 March 2014

  2. Sec. 8.8: Improper Integrals

  3. Sec. 8.8: Improper Integrals The integrals are improper because their bounds are infinity. The integrals are improper because they have a finite number of infinite discontinuities.

  4. Sec. 8.8: Improper Integrals

  5. Sec. 8.8: Improper Integrals Ex: Evaluate

  6. Sec. 8.8: Improper Integrals Ex: Evaluate

  7. Sec. 8.8: Improper Integrals Ex: Evaluate

  8. Sec. 8.8: Improper Integrals Ex: Evaluate

  9. Sec. 8.8: Improper Integrals Ex: Evaluate

  10. Sec. 8.8: Improper Integrals Ex: Evaluate

  11. Sec. 8.8: Improper Integrals Ex: Evaluate

  12. Sec. 8.8: Improper Integrals A Different Approach Ex: Evaluate A previous problem had this integral. We found the answer to be "∞." We can use the last part of the Definition of Improper Integrals with Infinite Discontinuities, "… the improper integral on the left diverges if either of the improper integrals on the right diverge" to conclude that this diverges (∞).

  13. Sec. 8.8: Improper Integrals Ex: Evaluate

  14. Sec. 8.8: Improper Integrals Ex: Evaluate Let u = 1 – xdv = e −xdx −du = dxv = −e −x

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