推 nobody1008:對不起我剛打了是dydx不是dxdy但還是 121.254.89.10 07/14 22:01
→ nobody1008:謝謝 121.254.89.10 07/14 22:02
→ j0958322080:那就做變換然後再直接積 61.58.92.27 07/15 06:19
→ nobody1008:是1嗎?? 121.254.89.10 07/15 11:47
※ 引述《nobody1008 (路人)》之銘言：
: 2 π/2
: S S ysin(xy) dx dy
: 1 0
: 要怎麼算阿= =
: 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
※ 編輯: j0958322080 來自: 123.0.209.150 (07/14 17:16)