Instructor Hentzel
Office Phone: 515-294-8141
E-mail:   hentzel@iastate.edu
Math Department Fax:      515-294-5454
http://orion.math.iastate.edu/hentzel/class.166.05


Textbook: Calculus by Varberg, Purcell, Rigdon, eight edition.


Practice test.  The real test is Monday, February 14, 2005 

              2      5
1.   INT   x(x  + 1 )    dx
        


             x
            e
2.   INT  ------  dx
               x
          1 + e



            Sin[Sqrt[x]]
3.   INT  ---------------  dx
             Sqrt[x] 



              Cos[x]
4.   INT  ---------------   dx
                   2
            1 + Sin [x]



             2 
5.   INT  Sin [x]  Cos[x]  dx




             3
6.   INT  Sec [x]  Tan[x] dx





             4       
7.   INT  Sec [x] Tan[x] dx




                    2/5
8.    INT    x (x+1)    dx









In problems 9 through 11,  Draw the triangle, and make the appropriate

substitution.  Do not integrate.





                 dx 
9.     INT    ---------
                2       2
               x  Sqrt[x -1]







                     dx 
10.    INT    ---------------
                2       2
               x  Sqrt[x +1]








                      2
             Sqrt[ 4-x  ]
11.    INT   -------------  dx
                   x 







                                                            n
12.    Derive the reduction formula for computing    INT Sin [x]  dx.






                                     u      v
In problems 13 through 16,   give             , and make the appropriate
                                    du     dv
substitution.  Do not integrate.






             3  x
13.   INT   x  e   dx








14.   INT   Sin[ln(x)] dx 







                     3 
15.   INT  (  ln(x) )   dx







16.   INT  ArcTan[x] dx






      

17.  Set up the terms of the partial fraction decomposition but

do not solve for the unknowns.

                3    2
              3x  + x + 1
     INT   ----------------
                2   2
           (x-1)  (x +3x+5)



18.  Set up the terms of the partial fraction decomposition and

solve for the unknowns.

             2
           3x  + 1
      INT ------------  dx
         (x-1)x(x+1)





In problems 19-20, complete the square and substitute u in for x-c.  

Do not integrate


                dx
19.   INT  ------------
                        2
           Sqrt[16+4x-2x  ]





                dx
20.   INT ----------------
             2
            x  + 4 x + 2