[微積] 用不同方法積分 可是答案不同?
Question : 試計算 Z^2 = X^2 + Y^2 , 0 <= Z <= 4 之體積
(1) 用切片法算
假設將他改躺在X'Y'平面的椎狀體積
b
S Pi* [f(x)]^2 dx
a
4 |4
S Pi* x^2 dx = Pi* x^3 /3 | = 64Pi/3
0 |0
(2) 用雙重積分+極座標
2Pi 4
S S z dA = S S r* rdrd@ = S S r^2 drd@ = 128Pi/3
0 0
第一個做法的答案是正確的
可是我想不出第二個做法為什麼會錯誤
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