Re: [積分] 一題台大的B卷考古題
∞ ∞ -(x^2+y^2)
∫ ∫ e dxdy
0 0
π/2 ∞ -r^2 π/2 1
= ∫ ∫ r‧e drdθ = ∫ --- dθ = π/4
0 0 0 2
∞ -x^2 ∞ -y^2 ∞ ∞ -(x^2+y^2)
∵ ( ∫ e dx ) ‧ ( ∫ e dy ) = ∫ ∫ e dxdy
0 0 0 0
∞ -x^2
∴ ∫ e dx = √π / 2
0
∞ -x^2 ∞ -x^2
→ ∫ e dx = 2 ‧ ∫ e dx = √π
-∞ 0
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 218.161.123.208
推
10/05 08:20, , 1F
10/05 08:20, 1F
推
10/05 08:39, , 2F
10/05 08:39, 2F
→
10/06 21:40, , 3F
10/06 21:40, 3F
→
10/06 21:41, , 4F
10/06 21:41, 4F
→
10/06 21:41, , 5F
10/06 21:41, 5F
推
10/07 05:03, , 6F
10/07 05:03, 6F
推
10/10 00:55, , 7F
10/10 00:55, 7F
→
10/10 00:56, , 8F
10/10 00:56, 8F
討論串 (同標題文章)
完整討論串 (本文為第 2 之 2 篇)：