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AP Calculus BC Wednesday, 19 February 2014

AP Calculus BC Wednesday, 19 February 2014. OBJECTIVE TSW (1) finish the test over sec. 7.1 – 7.4, 10.3, and 10.5, and (2) review procedures for fitting an integrand to one of the basic integration rules. You will have 30 minutes to complete the test.

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AP Calculus BC Wednesday, 19 February 2014

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  1. AP Calculus BCWednesday, 19 February 2014 • OBJECTIVE TSW (1) finish the test over sec. 7.1 – 7.4, 10.3, and 10.5, and (2) review procedures for fitting an integrand to one of the basic integration rules. • You will have 30 minutes to complete the test. • You may NOT go back to yesterday’s portion. • FRIDAY ASSESSMENT: Cake Lab.

  2. Sec. 8.1: Basic Integration Rules

  3. Sec. 8.1: Basic Integration Rules Sorry to say, but in Chapter 8, we're back to integrating the old-fashioned way . . . by hand.

  4. Sec. 8.1: Basic Integration Rules Many times, the key to integrating is to recognize the proper technique to use. Slight differences in the integrand can lead to very different integration techniques. long division arctan natural log

  5. Sec. 8.1: Basic Integration Rules u-substitution arcsin Ex: Evaluate Let u = 4 – x 2 du = −2xdx −½ du = xdx

  6. Sec. 8.1: Basic Integration Rules Ex: Evaluate Let u = e −2x du = −2e −2xdx − ½ du = e −2xdx − ½ du = dx / e2x

  7. Sec. 8.1: Basic Integration Rules Ex: Evaluate Let a = 4, u = x 3 du = 3x 2dx ⅓ du = x 2dx

  8. Sec. 8.1: Basic Integration Rules Ex: Evaluate Let u = 1 + ex du = exdx

  9. Sec. 8.1: Basic Integration Rules Ex: Evaluate Let u = ln(sin x) du = cos x / sin xdx du = cot xdx

  10. Sec. 8.1: Basic Integration Rules Ex: Evaluate Let u = 2x du = 2 dx ½ du = dx

  11. Sec. 8.1: Basic Integration Rules Procedures for Fitting Integrands to Basic Rules Expand (numerator): Separate numerator: Complete the square: Divide improper rational function:

  12. Sec. 8.1: Basic Integration Rules Procedures for Fitting Integrands to Basic Rules Add and subtract terms in numerator: Use trigonometric identities: Multiply and divide by Pythagorean conjugate:

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