1. AP Calculus BC Wednesday, 09 March 2016 OBJECTIVE TSW (1) solve integrals using trig substitution, and (2) quiz over basic integration rules and integration by parts. ASSIGNMENT DUE –Integration by Parts  wire basket ASSIGNMENTS DUE FRIDAY, 03/11/16 –Trigonometric Integrals –WS Integrals of Sine-Cosine Products TODAY’S ASSIGNMENT (due Monday, 03/22/16, but turn in on Friday, 03/11/16) –Trigonometric Substitution REMINDERS Friday, 11 March 2016 –PI Day Celebration: Friday, 11 March 2016

2. AP Calculus BC Thursday, 10 March 2016 OBJECTIVE TSW (1) solve integrals using trig substitution, and (2) quiz over basic integration rules and integration by parts. ASSIGNMENT DUE –Integration by Parts  wire basket ASSIGNMENTS DUE TOMORROW, 03/11/16 –Trigonometric Integrals –WS Integrals of Sine-Cosine Products TODAY’S ASSIGNMENT (due Monday, 03/22/16, but turn in tomorrow, 03/11/16) –Trigonometric Substitution REMINDERS Friday, 11 March 2016 –PI Day Celebration: Friday, 11 March 2016

3. Trigonometric Substitution (due Monday, 03/22/16)* Evaluate the following integrals. Evaluate the following definite integrals. *I would suggest turning this in on Friday!!!

4. Trigonometric Substitution

5. The idea of this section is to evaluate integrals with radicals of the form This will be done using the three Pythagorean identities:

6. 1)For integrals involving Trigonometric Substitution (a > 0) Trigonometric Substitution 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.

7. Trigonometric Substitution Ex:Evaluate: 3 x θ

8. 2)For integrals involving Trigonometric Substitution (a > 0) Trigonometric Substitution a 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.

9. Trigonometric Substitution Ex:Evaluate: θ 1 2x2x

10. 3)For integrals involving Trigonometric Substitution (a > 0) Trigonometric Substitution a 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.

11. Trigonometric Substitution Ex:Evaluate: θ x

12. Trigonometric Substitution Ex:Evaluate: θ x

13. Trigonometric Substitution Ex:Evaluate: θ x 2

14. Trigonometric Substitution Ex:Evaluate: θ x

15. Trigonometric Substitution Ex:Evaluate: θ x – 2 Completing the Square 2

16. QUIZ: Basic Integration Rules, Integration by Parts You may use a calculator. You have the remainder of the period to take the quiz. ASSIGNMENTS DUE FRIDAY, 03/11/16  Trigonometric Integrals  WS Integrals of Sine-Cosine Products (due Monday, 03/21/16, but suggested to turn in on Friday, 03/11/16)  Trigonometric Substitution (due Monday, 03/21/16, but suggested to turn in on Friday, 03/11/16) Sallie says, “Take my quiz!!”

17. QUIZ: Basic Integration Rules, Integration by Parts You may use a calculator. You have the remainder of the period to take the quiz. ASSIGNMENTS DUE TOMORROW, 03/11/16  Trigonometric Integrals  WS Integrals of Sine-Cosine Products (due Monday, 03/21/16, but suggested to turn in tomorrow, 03/11/16)  Trigonometric Substitution (due Monday, 03/21/16, but suggested to turn in tomorrow, 03/11/16) Sallie says, “Take my quiz!!”