Re: [微積] 微積分

[LuisSantos (但願真的能夠實現願望)]

※ 引述《yourfriend (祈禱)》之銘言：
: 對不起，微積分爛掉了= =
: 請較一題
:   r
: ∫ √(r^2-x^2) dx
:  -r
: 可否麻煩幫忙提點一下這小問題= =謝謝喔!!
'


令 x = rsinθ , 則 dx = rcosθ dθ


x = r  =>  rsinθ = r  =>  sinθ = 1  => θ = π/2


x = -r =>  rsinθ = -r =>  sinθ = -1 => θ = -π/2


    r
   ∫ √(r^2 - x^2) dx
    -r

    π/2
=  ∫     (r)(cosθ)(r)(cosθ) dθ
    -π/2

    π/2
=  ∫     (r^2)((cosθ)^2) dθ
    -π/2

    π/2         1 + cos2θ
=  ∫     (r^2)(------------) dθ
    -π/2            2

           θ    sin2θ |π/2
=   (r^2)(--- + -------)|
           2       4    |-π/2

     (π)(r^2)
=   -----------
          2



--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 114.36.170.99
→ yourfriend  :感恩!!!