Re: [微積] 微積分
※ 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
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03/25 08:50, , 1F
03/25 08:50, 1F
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