Question

Lilly

請問這題為什麼只能先對y積分？只是因為先對x的話積不出來嗎？

Evaluate the double integral: f(x, y) = ye; R is bounded by x=2
2
and y=0.
ud hisborod【107 東吳巨資】
解:積分區域R如圖,只能先對 y 積分
s! Si yet" dx dy
- Syex! + dy
3X²
So ye. 314² dy
4
= site dy
A
R
x = |
2x
y=2x
[[ ye²d4 = ['ƒ”ª" ye^¹ dydx = ['-—- y^²e²" d
dx
R
|y=0
y
4
y=2x
28²e²dx=3e²-3(e-1).
= S₁ 2x² e ³ dx = 2²/
#gesidgate enyi lo-te
3
==
X
YOY'S
nll
>
x = 1
1:2

積分 重積分

Answer 1

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Alstormeria5

Here

Lilly

I see. thanks~