數學高微的問題麻煩一下~~

👨🏻‍🏫 學術台數學

[匿名]

2010-04-20 6:54 am

Compute 積分 F * dx for the following F and C ( C 應該是上下界的區域 ) :
F(x,y)=( x^2 * y , x^3 * y^2) ; C is closed curve formed by portions of the line y = 4 and the parabola y = x^2 , oriented counterclockwise.

更新1:

是的，不好意思，的確是積分 F (dot) dx

更新2:

正確答案是9856/45，可是我不知道怎麼算的

更新3:

請問您的-128/15的算式是？

回答 (3)

天助

2010-04-21 7:18 am

✔ 最佳答案

∫_c (x^2y dx+x^3y^2 dy)
(Green's thm) = ∫[-2~2]∫[x^2~4] x^2(3y^2-1)dy dx
=∫[-2~2] x^2[64-x^6-4+x^2] dx
=∫[-2~2] (-x^8+x^4+60x^2) dx
=2 (-x^9/ 9+ x^5/5 + 20x^3) 代x=0~2
=2 (-512/9 + 32/5 + 160)
= 9856/45

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[匿名]

2010-04-20 8:21 am

-128/15

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教書的

2010-04-20 7:24 am

Do you mean "積分 F * dx " the line integral of the vector field F along C?
i. e. 積分 F (dot) dr? or something else?

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收錄日期: 2021-04-30 14:40:47
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