題目:
Please find the area ofthe region bounded by x-axis and one arch of the
cycloid(擺線) given by: x=a(t-sint) and y=a(1-cost)
答案: A =∫ y dx
2π
=∫ a(1-cost) d(a(t-sint))
0
2
= 3πa
問題: A =∫ y dx <=? 上下限0-2π <=?
題目3:
x i -z j +y k
Let vector field F = ------------------
x^2 + y^2 + z^2
the posiion vector r = xi + yj + zk and the line path C be on the plane x=0
and the extend from the point (0 1 0) to the point (0 -2 0). Are the line
integrals ∫ F˙dr and ∫ F ╳ dr independent of path?
c c
問題: ......................
故若C為yz平面上不含原點的區域中的任意曲線時 該積分值與路徑無關 且
(0 -2 0) z z |(0 -2 0)
I = ∫ d (tan^-1 ---) = tan^-1 ----- | = -π
(0 1 0) y y |(0 1 0)
︿︿︿︿︿︿
y
就是我積出來的 -tan^-1 ----- 是積錯嗎? 然後若照課本答案將上下限帶入
z
0 0
tan^-1 ----- -tan^-1 ------ = -π <= 這樣不是會變0嗎 -π是?
1 -2
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※ 編輯: bizzard 來自: 114.35.149.203 (10/20 23:51)