工程數學,積分面積

2015-01-16 8:01 pm
The area enclosed by two vectors dr1 and dr2 is dA=|dr1xdr2|.

Questions:

a. The surface Σ is given by z=z(x,y). Derive the area dσ of the lateral surface in terms of dx and dy.

b. Calculate ʃʃ(Σ)(x^2+y^2)dσ, where the surface is given by z=16-x2-y2 lying between x^2+y^2=1 and x^2+y^2=9


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更新1:

想請問,b小題的第二行變第三行 r^2=x^2+y^2 從x^2+y^2=1積到x^2+y^2=9 dxdy怎麼代換成rdr

回答 (2)

2015-01-17 6:21 am
✔ 最佳答案

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希望有幫助到你喔 :D
參考: 我的小腦袋瓜ㄦ
2015-01-17 2:28 am
(a) should start with r = (x, y, z(x,y) )
r_x = (1, 0, z_x)
r_y = (0, 1, z_y)
r_x X r_y = - z_y i - z_x j + k
|r_x X r_y| = sqrt(1 + z_x^2 + z_y^2)


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