1. (48 pt) Evaluate the following:

a) b) c)

d) e) f)

2. (10 pt) Find the area between the curves and .

3. (10 pt) Find the volume obtained by revolving the region bounded by and about the line y=1.

4. (10 pt) Show that the volume of a right circular cylinder of base radius R and height h has volume given by the formula: V=(1/3)p R²h.

5. (12 pt) Consider the function defined by if and if . Find the average value of on the interval [-p ,1]. Is there a value (say c) in [-p ,1] such that ? Does this contradict the mean value theorem for integrals?

6. (10 pt) Let be a differentiable function such that and . Find

7. EXTRA CREDIT (5 pt) Let . Find