MATH 161

EXAM 2

 

 

 

  1. (10 pt) For each of the following, write down the partial fractions decomposition form. You do not have to solve for the constants:

    2.  

    a) b)

     

  2. (12 pt) For each of the following, suggest a substitution or technique that will help to solve the integral. Briefly state why your substitution or technique should work.

    3.  

     

    a) b)where is an integer

     

    c) d)

     

  3. (32 pt) Evaluate the following integrals:

    4.  

    a) b)

     

    c) d)

     

  4. (8 pt) Find the surface area of a sphere of radius 2.

    5.  

  5. (8 pt) Find the length of the parabola from the points (1,1) to (4,-2).

    6.  

  6. (8 pt) Solve the differential equation (hint: first let ).

    7.  

  7. (8 pt) Describe the curve given by the parametric equations .

    8.  

  8. (14 pt) Use Simpson’s Rule with n=4 to estimate
and use the error estimate to find the maximum error. Check your answer. Guess the error for the trapezoid rule and the midpoint rule (without using the error estimates).

 

SOME USEFUL STUFF:

 

TRIGONOMETRIC IDENTITIES:

 

SOME ANTIDERIVATIVES:

 

MISCELLANEOUS:

 

If , then , , .

.

 

where is the midpoint of the ith subinterval.

 

(n:even).

 

where for all .