推 vu3cj0su3:我算的跟你一樣 不過答案是Pi/60 61.230.149.53 12/20 22:47
→ vu3cj0su3:有可能是答案錯了=.= 61.230.149.53 12/20 22:47
→ coolbaby119:請問這叫什麼法?x=...y=...d=..看不懂 134.208.34.188 12/23 19:54
→ coolbaby119:這應該不是殼法或圓盤法吧..不清楚 134.208.34.188 12/23 19:55
※ 引述《vu3cj0su3 ()》之銘言：
: Let R be the region bounded by y=x^2 and y=x.
: Find the volume of solid that results when R is revolved around
: the line y=x
: [註 因為還沒學甜甜圈定理及多重積分...so 除了座標軸變換外 可以用
: disk or shell把這題做出來嗎? ]
1 1 1 2 1 1 1
A = ∫ (x-x^2) dx = ∫ x dx - ∫ x dx = --- - --- = ---
0 0 0 2 3 6
1
∫ x(x-x^2)dx
_ 0 1/12 1
x = -------------- = ----- = ---
A 1/6 2
1 1
---∫(x^2-x^4)dx
_ 2 0 1/15 2
y = ----------------- = ----- = ---
A 1/6 5
|(1/2)-(2/5)| √2
d = --------------- = ---
√[(1^2+(-1)^2] 20
1 √2 √2
V = A(2πd) = --- (2π* ---- ) = ----π
6 20 60
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