Math231       Exam 1  (continued)                       Spring, 2018

 

 

        ∞

10.    ∫ (e-2x x2018 dx                                                   Answer:  Converges

        1

 

      ∞

11.  ∫ (1/xp) dx where  p ≥ 1                                      Answer:  Diverges

      1

 

 

           ∞

12.      ∫ [ ( 2x4 + 10 } / {x6 + 2x + 20 }] dx         Answer:   Converges

          1

 

 

13.  Evaluate   ∫ [ √ (4-x2) / x2 ] dx                      Answer:  arccos(x/2) - √(4-x2)/x  + C

 

                        3

14.  Evaluate   ∫ [ (x+9) / (x2+3x - 4) ] dx           Answer:  ln|24/7|

                       2

 

Express result with only one term.

 

 

 

15.  Evaluate the improper integral or show that it diverges.

 

                        ∞

                        ∫   3x2e-x  dx                        Answer:   I = 6,    Converges

                       0