Re: [方法] 100年成大第6題
※ 引述《kylestyle (最近有點煩)》之銘言：
: Find the average value of f(x,y) = xy over the quarter circle
: x^2 + y^2 ≦ 1 in the first quadrant
: 求板上大大解答
By definition, the average value is given by
_ 1
f = -----∫∫f(x,y)dA
A(Ω) Ω
where Ω = {(x,y) | x^2+y^2≦1, x≧0, y≧0}
and A(Ω) denotes the area of Ω. Thus
_ 4 1 π/2
f = --- ∫∫r^2 cosθsinθ r dθ dr
π 0 0
4 r^4|1 cos 2θ |π/2
= --- ---| (- --------)|
π 4 |0 4 |0
= 1/2π
有錯請指正 m(_ _)m
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 59.115.146.209
推
06/24 18:36, , 1F
06/24 18:36, 1F
推
06/24 18:41, , 2F
06/24 18:41, 2F
→
06/24 18:42, , 3F
06/24 18:42, 3F
→
06/24 18:42, , 4F
06/24 18:42, 4F
→
06/24 18:45, , 5F
06/24 18:45, 5F
→
06/24 18:46, , 6F
06/24 18:46, 6F
推
06/24 18:51, , 7F
06/24 18:51, 7F
討論串 (同標題文章)
本文引述了以下文章的的內容：
完整討論串 (本文為第 2 之 2 篇)：