devotion & mathematics

  Leibnitz-Test : Problems & Solutions :                             *       Examine the character of the series Σ (-1) n-1 n /2n-1                                    Back                                                  Solution :   *      Examine the convergence of 1/1.2 – 1/3.4 + 1/5.6 -1/7.8 +…        Solution : *            Examine the convergence of Σ (-1) n 1/n ( 1+ 1/2 + 1/3+ …+ 1/n). Solution : *   Prove that   1- 1/2 + 1/3 - … converges. Solution : *      Prove that Σ (-1) n / n! = 1- 1/1! + 1/2! - 1/3!+… converges. Solution :  Leibnitz-Test : #Problems #...

 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 :            ...