English Deutsch Français Italiano Español Português 繁體中文 Bahasa Indonesia Tiếng Việt ภาษาไทย
All categories

Here is the equation..sorry i couldn't find a way to paste it
http://img3.freeimagehosting.net/image.php?63beb02fc0.jpg

change the order of integration from dydx to dxdy

Thanks!

2007-10-26 07:14:28 · 4 answers · asked by dkmu 1 in Science & Mathematics Mathematics

4 answers

The region of integration is the triangle bounded by y = x, y = -x, and x = 2. To integrate w.r.t. x first, the limiting curves change at y=0, so you have to split into two integrals. For -2<=y<=0, you have x from -y to 2, and for 0<=y<=2, you have x from y to 2. The integral with order of integration interchanged is

Int(y from -2 to 0) Int(x from -y to 2) integrand dx dy
+ Int(y from 0 to 2) Int(x from y to 2) integrand dx dy.

2007-10-26 07:25:10 · answer #1 · answered by acafrao341 5 · 0 0

I find that I really need to draw a picture of the region of integration to help me invert the order of integration.

You will need to break this into two double integrals. Note that for -2
So for one double integral, (outer integral) y goes from -2 to 0 and (inner integral) x goes from -y to 2; for the other double integral, (outer integral) y goes from 0 to 2 and (inner integral) x goes from y to 2. (And obviously you add these two.)

2007-10-26 07:34:32 · answer #2 · answered by Ron W 7 · 1 0

Just switch the integration limits from the inner and outer with each other and do the "dx" integration first, treating terms in "y" as constants.
The intergrands don't look all that difficult.

2007-10-26 07:27:23 · answer #3 · answered by cattbarf 7 · 0 2

?[0,3] ?[x, 3] sin(y)*cos(x/y)/y dy dx changing the order of integration: ?[0,3] ?[0, y] sin(y)*cos(x/y)/y dx dy = ?[0,3] sin(y)/y * y*sin(x/y) eval. from x = 0 to x = y dy = ?sin(y) * (sin(a million) dy = -sin(a million)*[cos(3) - a million] = sin(a million)*(a million - cos(3))

2016-10-14 02:58:15 · answer #4 · answered by ? 4 · 0 0

fedest.com, questions and answers