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AP Calculus BC Monday, 24 February 2014

AP Calculus BC Monday, 24 February 2014. OBJECTIVE TSW (1) find an antiderivative using integration by parts, and (2) use a tabular method to perform integration by parts. ASSIGNMENTS Sec. 8.1: p. 522 (1, 3, 15-31 odd, 33-49 odd) Due: Tomorrow (2/25/14)

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AP Calculus BC Monday, 24 February 2014

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  1. AP Calculus BCMonday, 24 February 2014 • OBJECTIVE TSW (1) find an antiderivative using integration by parts, and (2) use a tabular method to perform integration by parts. • ASSIGNMENTS • Sec. 8.1: p. 522 (1, 3, 15-31 odd, 33-49 odd) Due: Tomorrow (2/25/14) • Sec. 8.2: pp. 531-532 (11-39 eoo, 47-57 odd, 59-64 all) Due: Wednesday/Thursday (02/26-27/14) • Sec. 8.3: p. 540 (5-17 odd, 43, 44, 51-54 all, 65, 69, 70)Due: Monday, (03/03/14) • WS Sec. 8.3 Due: Monday (03/03/14) • QUIZ ON MONDAY, 03/03/14 • Sec. 8.1 – 8.3. • PIDay will be celebrated on Friday, 14 March 2014. • Be thinking about what “pie” you would like to bring. Calendars are not ready – copy these assignments. Tests will be returned after the lesson.

  2. Sec. 8.2: Integration by Parts

  3. Sec. 8.2: Integration by Parts From Sec. 8.1

  4. Sec. 8.2: Integration by Parts For the most part, these do not involve products. “Integration by parts” is basically used for products.

  5. Sec. 8.2: Integration by Parts

  6. Sec. 8.2: Integration by Parts Ex: Let u = xdv = exdx du = dxv = ex

  7. Sec. 8.2: Integration by Parts Ex: Let u = arccos xdv = dx v = x Let w = 1 – x 2 dw = −2xdx ½ dw = −xdx

  8. Sec. 8.2: Integration by Parts Ex: Now use algebra! Let u = sin 2xdv = exdx du = 2cos 2x dxv = ex Let w= cos 2xdz= exdx dw= −2sin 2x dxz= ex

  9. Sec. 8.2: Integration by Parts Ex: Let u = x 2dv = cos xdx du = 2x dxv = sin x Let w= xdz= sin xdx dw= dxz= −cosx

  10. Sec. 8.2: Integration by Parts Tabular Method + − + − When u gets to 0, stop and determine the answer. +

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