Re: [積分] 海洋大學101轉學考

[BaBi (迅雷不及掩耳盜鈴)]

     4     x^2
   ∫  ------------dx
     0   √(2x+1)

--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 36.229.65.169
→ yhliu:設 u=√(2x+1), x=(u^2-1)/2, 1≦u≦3 即可.

        Let u^2 = 2x+1, 2udu = 2dx , udu = dx

            x = (u^2-1)/2 , x^2 = (1/4)(u^4-2u^2+1)


                      3
        原式 = (1/4) ∫ (u^4-2u^2+1) du
                      1
                                                |3
             = (1/4) [ (u^5)/5 - (2u^3/3) + u ] |
                                                |1

             = 124/15

--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 114.46.136.60