[微積] Integral problem

看板Math作者 (聖なるエンジェル)時間12年前 (2013/11/11 12:45), 編輯推噓5(503)
留言8則, 4人參與, 最新討論串1/1
b ∫xdx/[(x^2-a^2)(b^2-x^2)]^(1/2)=? a 題目如上 求解法 參考書只給答案pi/2 但不知其所以然 用了integration by part或代換法還是找不到解法 請各位大大幫忙 感謝 -- Chaos Destroyer -Envoy of the Demise- Effect LIGHT Fairy LV10 ATK0 DEF0 Cannot be Normal Summoned or Set. Must First Special Summoned (from your hand or your graveyard) by destroying all the card on the field and either players' hand. When this card is Special Summoned, neither player can activate any cards or effects. Once per turn: You can inflict damage equals opponent's Life Points. During your Main Phase: You can reveal this card from your hand; sent -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 140.115.189.30

11/11 13:16, , 1F
令y=x^2-a^2變數變換,原積分就是beta函數
11/11 13:16, 1F

11/11 13:17, , 2F
可算出β(0.5,0.5)/2=pi/2
11/11 13:17, 2F

11/11 13:21, , 3F
更正,令y=(x^2-a^2)/(a^2+b^2)
11/11 13:21, 3F

11/11 13:23, , 4F
唉,一直打錯,是b^2-a^2才對
11/11 13:23, 4F

11/11 13:31, , 5F
請問題目的積分是對整個式子還是只有x?
11/11 13:31, 5F

11/11 14:01, , 6F
整個式子吧, 被積函數是分數式時把dx寫在分子滿常見
11/11 14:01, 6F

11/11 14:28, , 7F
是積分符號的位置讓我誤會了
11/11 14:28, 7F

11/19 15:15, , 8F
ty
11/19 15:15, 8F
文章代碼(AID): #1IW63esv (Math)