# AP Calculus BC Friday, 28 February 2014

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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 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
• Sec. 8.4: Trigonometric SubstitutionSec. 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:
• Sec. 8.4: Trigonometric Substitution1) For integrals involvingTrigonometric Substitution (a > 0)au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.Sec. 8.4: Trigonometric SubstitutionEx: Evaluate: 3xθSec. 8.4: Trigonometric Substitution2) For integrals involvingTrigonometric 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.aSec. 8.4: Trigonometric SubstitutionEx: Evaluate: 2xθ1Sec. 8.4: Trigonometric Substitution3) For integrals involvingTrigonometric 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.aSec. 8.4: Trigonometric SubstitutionEx: Evaluate: xθθSec. 8.4: Trigonometric SubstitutionEx: Evaluate: xθSec. 8.4: Trigonometric SubstitutionEx: Evaluate: x2θSec. 8.4: Trigonometric Substitutionx – 2Completing the SquareEx: Evaluate: 2
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