Clicker Question 1 What is ? – A. 1 / (2  (x 2 + 4)) + C – B. 1 / (4  (x 2 + 4)) + C – C. x / (2  (x 2 + 4)) + C – D. x / (4  (x 2 + 4)) + C – E.  (x 2 + 4) / x + C

Clicker Question 2 What is ? – A. 3/2 – B.  / 6 – C. 1 /  3 – D.  / /  3 – E.  3

Antidifferentiation Strategies (9/29/10) 1. Is the integrand immediately recognizable in terms of our basic antidifferentiation facts? 2. If no, can it be algebraically manipulated into a simpler form? 3. If no, can a u-substitution be used? 4. If no, is it a product of two parts, one of which has a “nice” derivative and the other a “not too bad” antiderivative? Then try integration by parts.

Strategies Continued Does it have something of the form a 2  x 2 ? Then a trig substitution may be helpful. All else failing, you may be able to get an answer from computer software (e.g., Mathematica) or tables (e.g., in our text). Remember that if it is a definite integral you want to evaluate, you do not have to use the Fundamental Theorem! You can always do numerical (approximate) integration. This is where we will turn next.

Assignment for Friday Read Section 7.5. Note that we have not covered all the ideas which are summarized here; for example, we have not done “partial fraction technique” and we’ve not done hyperbolic functions (sinh, cosh, etc.). On page 488, see if you can do Exercises 1, 5, 7, 9, 14, 19, 20, and 27.