1. OBJECTIVE TSW (1) evaluate improper integrals, and (2) review for the test covering integration techniques. ASSIGNMENT DUE TOMORROW, FRIDAY, 04/01/16 –Improper Integrals UPCOMING –TEST: Integration Techniques is tomorrow, Friday, 01 April 2016. AP Calculus BC Thursday, 31 March 2016

2. WS Integrals of Sine-Cosine Products 1)2) 3)4) 5)6) 7)8)

3. WS The Lostistics Curve 1)a)y = 5 b)L = 12c)k = 1 d)t = 0.336e) 2)a)y = 1b)L = 1000c)k = 0.9 d)t = 8.895e) 3)a)L = 10b)k = 10c)5 4)a)L = 50,000b)k = 50c)25,000 5)a)k = 0.115b) d) # infected day 0 5 10 14 93 20

4. TEST TOPICS – Integration Techniques Evaluate integrals  Basic integration  Integration by parts Let the "easily integrated" part be dv and the "easily derivatized" part be u.

5. TEST TOPICS – Integration Techniques Evaluate integrals (continued)  Integrals with powers of sine and/or cosine Convert cos 2 θ and sin 2 θ to “usable” forms.  Integrals with sine and/or cosine of differing arguments "Sally Says: Charge My Card" "Sally Can Sing Pig Songs" "Cousin Carl Collects Pork Cars"

6. TEST TOPICS – Integration Techniques Evaluate integrals (continued)  Trigonometric substitution and integration  Partial fractions (linear, multiplicity one)

7. TEST TOPICS – Integration Techniques Solve logistic curve problems. Use l’Hôpital’s Rule to evaluate limits. Evaluate improper integrals  Infinite limits  Infinite discontinuities

8. TEST TOPICS – Integration Techniques Reminder:  Know the derivatives and integrals of the six trig functions and their inverses. The test will be part with calculator, part without.  When you take the test, MANAGE YOUR TIME ACCORDINGLY!!! Wear your FALCON CALCULUS t-shirt. Questions?