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AP Calculus BC Friday, 28 February 2014

AP Calculus BC Friday, 28 February 2014. OBJECTIVE TSW solve integrals using trig substitution. UPCOMING ASSIGNMENTS Sec. 8.3: p. 540 (5-17 odd, 43, 44, 51-54 all, 65, 69, 70) Due on Monday, 03 March 2014. Sec. 8.4: p. 549 (5-16 all, 21-41 eoo , 43, 45, 53, 54)

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AP Calculus BC Friday, 28 February 2014

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  1. AP Calculus BCFriday, 28 February 2014 • OBJECTIVETSW solve integrals using trig substitution. • UPCOMING ASSIGNMENTS • Sec. 8.3: p. 540 (5-17 odd, 43, 44, 51-54 all, 65, 69, 70) • Due on Monday, 03 March 2014. • Sec. 8.4: p. 549 (5-16 all, 21-41 eoo, 43, 45, 53, 54) • Due on Tuesday, 04 March 2014. • Sec. 8.5: p. 559 (1, 5-15 odd) • Due on Friday, 07 March 2014. • REMINDERS • PI Day Celebration: Friday, 14 March 2014

  2. Sec. 8.4: Trigonometric Substitution

  3. Sec. 8.4: Trigonometric Substitution • The idea of this section is to evaluate integrals with radicals of the form • This will be done using the three Pythagorean identities:

  4. Sec. 8.4: Trigonometric Substitution 1) For integrals involving Trigonometric Substitution (a > 0) a u  This looks like arcsin. The sin ratio is opposite / hypotenuse. "a" should go on the hypotenuse; "u" should go on the opposite side; the square root goes on the remaining side.

  5. Sec. 8.4: Trigonometric Substitution Ex: Evaluate: 3 x θ

  6. Sec. 8.4: Trigonometric Substitution 2) For integrals involving Trigonometric Substitution (a > 0) u  This looks like arctan. The tan ratio is opposite / adjacent. "a" should go on the adjacent side; "u" should go on the opposite side; the square root goes on the remaining side. a

  7. Sec. 8.4: Trigonometric Substitution Ex: Evaluate: 2x θ 1

  8. Sec. 8.4: Trigonometric Substitution 3) For integrals involving Trigonometric Substitution (a > 0) u  This looks like arcsec. The sec ratio is hypotenuse / adjacent. "a" should go on the adjacent side; "u" should go on the hypotenuse; the square root goes on the remaining side. a

  9. Sec. 8.4: Trigonometric Substitution Ex: Evaluate: x θ

  10. θ Sec. 8.4: Trigonometric Substitution Ex: Evaluate: x

  11. θ Sec. 8.4: Trigonometric Substitution Ex: Evaluate: x 2

  12. θ Sec. 8.4: Trigonometric Substitution x – 2 Completing the Square Ex: Evaluate: 2

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