作者j0958322080 (Tidus)
看板trans_math
标题Re: [考古] 逢甲98微积分一题
时间Thu Jul 14 17:15:34 2011
※ 引述《nobody1008 (路人)》之铭言：
: 2 π/2
: S S ysin(xy) dx dy
: 1 0
: 要怎麽算阿= =
: 算好久
let xy = u, du = ydx, when x = 0, u = 0, x = π/2, u = yπ/2
2 π/2 2 πy/2 2 yπ/2
∫ ∫ ysin(xy) dx dy = ∫ ∫ sinu du dy = ∫(-cosu)| dy
1 0 1 0 1 0
2 2 2
∫[1-cos(yπ/2)]dy = ∫dy - ∫[cos(yπ/2)]dy, let k = yπ/2, dk = dyπ/2
1 1 1
2 2 2
1 - ---∫cosk dk = 1 - --- (sin2 - sin1)
π 1 π
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◆ From: 123.0.209.150
※ 编辑: j0958322080 来自: 123.0.209.150 (07/14 17:16)
1F：推 nobody1008:对不起我刚打了是dydx不是dxdy但还是 121.254.89.10 07/14 22:01
2F：→ nobody1008:谢谢 121.254.89.10 07/14 22:02
3F：→ j0958322080:那就做变换然後再直接积 61.58.92.27 07/15 06:19
4F：→ nobody1008:是1吗?? 121.254.89.10 07/15 11:47