Re: [積分]90年考古
※ 引述《j19880706 (smallpig)》之銘言：
: 請教大大 我們還沒教過重積分
: 先寫考題 遇到瓶頸
: 所以來板上請教大大
: 1 1 3
: ∫ ∫ cos Y dy dx =
: 0 √x
: 這題怎麼解阿 Y的三次方
: 感謝大大熱心幫小弟解題
先把積分區域畫在xy座標圖上
R = {(x,y)|0≦x≦1 , √x ≦ y ≦ 1}
= {(x,y)|0≦y≦1 , 0 ≦ x ≦ y^2}
1 1
∫ ∫ cos(y^3) dy dx
0 √x
1 y^2
= ∫ ∫ cos(y^3) dx dy
0 0
1 |x = y^2
= ∫ (x)(cos(y^3)) | dy
0 |x = 0
1
= ∫ (y^2)(cos(y^3)) dy
0
1 |1
= (---)(sin(y^3)) |
3 |0
1
= (---)(sin1)
3
--
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