MATH 161

EXAM 2

 

  1. (10 pt) For the following two rational functions, show the partial fractions decomposition form.

    2.  

    a) b)

     

  2. (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).

    3.  

    a) (where is an integer) b)

     

    c) d)

     

  3. (20 pt) Evaluate the following integrals

    4.  

    a) b)

     

    c) d)

     

  4. (5 pt) Show that the integral converges (do not try to find an antiderivative of this).
  5. (10 pt) Solve the initial value problem ,
  6. (15 pt) Use Simpson’s Rule and an appropriate integral to estimate ln(3) with error smaller than .001.
  7. (20 pt) For the following problem consider the quarter circle bounded by , and
in the first quadrant.
  1. Find the centroid of this region (assuming constant density).
  2. Find the volume obtained when we revolve this region about the line
.
  1. EXTRA CREDIT (10 pt)
  1. Find a parametric equation that describes the ellipse
  2. 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
)