1. Look Ahead (4/27/08) Tuesday – HW#4 due at 4:45 Wednesday – Last class – return clickers, review and overview, and do evaluations. Thursday – Regular office hours 3:15-4:45 Friday – Extra help 2-3 pm, HW#4 back Monday 5/4 – Office Hours 1-3 pm; Exam 6-9 pm in Emerson

2. Clicker Question 1 What is an antiderivative of f (x ) = sin(x 2 ) ? A. cos(x 2 ) B. - cos(x 2 ) C. - cos(x 2 ) / 2x D. - cos(2x ) E.

3. Average value of a function on an interval To find the average value of a list of numbers, you add them up and divide by how much is there. It’s the exact same for functions: add up the values of the function on the interval in question and then divide by how much is there (i.e., the length of the interval). Thus the average value of f on [a, b] is

4. Example of average value What is the average value of sin(t) on the interval [0,  ] ? Look at the picture and make a guess. The answer is = 2 /  .637 Check that this answer makes sense.

5. Average height on a graph Given a graph of f (x) on some interval [a, b], the average value on a graph is the average height, i.e. the height whose rectangle has the same area as the area under the curve.) Example: Guess and then compute the average height (or value) of f (x) = x 2 on [0, 2].

6. Clicker Question 2 What is the average value of f (x) =  x on the interval [0, 4] ? A. 16/3 B. 4/3 C. 2 D. 8/3 E. 3

7. Assignment for Wednesday Find the average value of 1. f (x ) = e 2x on [0, 2] 2. f (x ) = x sin(x 2 ) on [0,  ] 3. f (x ) = 1/(1+x 2 ) on [0,  /2] 4. f (x ) =  (4 – x 2 ) on [-2, 2] (FTC too hard on #4. Recognize the curve!) BE HERE (with clicker)!