in the first quadrant.
- (10 pt) For the following two rational functions, show the partial fractions decomposition form.
- (20 pt) For the following integrals, tell what technique/substitution that you would use and briefly say why (you do not have to work the integrals out).
a) (where is an integer) b)
- (20 pt) Evaluate the following integrals
- (5 pt) Show that the integral converges (do not try to find an antiderivative of this).
- (10 pt) Solve the initial value problem ,
- (15 pt) Use Simpsonís Rule and an appropriate integral to estimate ln(3) with error smaller than .001.
- (20 pt) For the following problem consider the quarter circle bounded by , and
- Find the centroid of this region (assuming constant density).
- Find the volume obtained when we revolve this region about the line
- EXTRA CREDIT (10 pt)
- Find a parametric equation that describes the ellipse
- Find the surface area obtained when the above ellipse is revolved about the x-axis. Check your answer by taking the limit as . (You may assume that