Re: [微積] 幾個重積分的題目...拜託幫忙一下
看板Math作者WalterRudin (Mathematical Analysis)時間14年前 (2011/08/31 07:11)推噓3(3推 0噓 3→)留言6則, 5人參與討論串2/2 (看更多)
1) π x
∫ ∫ x sin y dydx
0 0
|x
= ∫ x (-cos y)| dx
|0
= ∫x (1-cos x) dx
= ∫x dx - ∫x cos x dx
using integral by parts we can find
∫x cos x dx = x sin x + cos x .
(you must figure out this by yourself)
The rest is trivial.
2) π π
∫ ∫ (sin y)/y dy dx
0 x
we know that ∫ (sin t)/t dt is difficult,
so we must change dydx to dxdy.
by Fubini's theorem,
π y
∫ ∫ (sin y)/y dy dx = ∫ ∫ (sin y)/y dx dy (why? think!)
0 0
π
= ∫ sin y dy
0
The rest is trivial.
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 203.66.179.6
→
08/31 07:18, , 1F
08/31 07:18, 1F
→
08/31 07:20, , 2F
08/31 07:20, 2F
推
08/31 14:17, , 3F
08/31 14:17, 3F
推
08/31 17:56, , 4F
08/31 17:56, 4F
→
08/31 18:01, , 5F
08/31 18:01, 5F
推
09/01 16:20, , 6F
09/01 16:20, 6F
討論串 (同標題文章)
完整討論串 (本文為第 2 之 2 篇)：