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                            Line Integrals                  Introduction                        Problems & Solutions                                                          Back #vector #calculus #vector calculus

 LINE INTEGRALS - PROBLEMS &SOLUTIONS :       We have discussed about the definitions and development of line integrals.  Here we going to solve some problems regarding line integrals.                      Back  PROBLEM 1 :  .   Evaluate  ∫ dx/(x+y),  Where C  is the curve x=at 2 ,y=2at, 0 ≤ t ≤ 2. SOLUTION :                          PROBLEM 2:   Show that ∫ xy dx  =4/5, where C is the arc of the parabola y 2 =x from (1,-1) to   (1,1). SOLUTION :                         3.   PROBLEM 3 :  Show that ∫  [ (x-y) 3 dx+(x-y) 3 dy]=3 πa 4 , where C Is the circle x 2 +y 2 =a 2  in       the counter clockwise sense.         SOLUTION :            ...