There is a a question about double integrals in http://www.shnkc.tk/double_int. The problem is that I couldn't get how we should start. Should we translate x and y to polar coordinates or something else? I am waitin g for your answers and suggestions.
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Calculus-Double integral
- Thread starter Shnkc
- Start date
akoaysigod
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- Oct 5, 2009
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I don't think you need polar coordinates for this. The region is a triangle with vertices (0,0), (0, -2) and (-1, 1) I'm fairly certain. The next part is where I'm still having trouble with these types of problems. I haven't really tried to do any until now though but...
D = {(x,y) | -1 =< x =< 0 , -x =< y =< x+2} or D = {(x,y) | 0 =< y =< 1 , y-2 =< x =< -y}
It could be either of these although I may have set them up wrong.
I'm pretty sure about the first part of the domain but not so much on the second one. I get confused on which its less than or greater than sometimes. I'm pretty sure the second domain is right but I don't know about the first. But anyway.
int[0,1] int[y-2, -y] f(x,y) dxdy
Someone else should check this but I know you don't need polar coordinates.
D = {(x,y) | -1 =< x =< 0 , -x =< y =< x+2} or D = {(x,y) | 0 =< y =< 1 , y-2 =< x =< -y}
It could be either of these although I may have set them up wrong.
I'm pretty sure about the first part of the domain but not so much on the second one. I get confused on which its less than or greater than sometimes. I'm pretty sure the second domain is right but I don't know about the first. But anyway.
int[0,1] int[y-2, -y] f(x,y) dxdy
Someone else should check this but I know you don't need polar coordinates.
BigGlenntheHeavy
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- Mar 8, 2009
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\(\displaystyle V \ = \ \int_{0}^{1}\int_{y-2}^{-y}[e^{\frac{y+x}{y-x}}]dxdy\)
\(\displaystyle or \ V \ = \ \int_{-2}^{-1}\int_{0}^{x+2}[e^{\frac{y+x}{y-x}}]dydx \ + \ \int_{-1}^{0}\int_{0}^{-x}[e^{\frac{y+x}{y-x}}]dydx\)
\(\displaystyle or \ V \ = \ \int_{-2}^{-1}\int_{0}^{x+2}[e^{\frac{y+x}{y-x}}]dydx \ + \ \int_{-1}^{0}\int_{0}^{-x}[e^{\frac{y+x}{y-x}}]dydx\)
BigGlenntheHeavy
Senior Member
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- Mar 8, 2009
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- 1,577
\(\displaystyle I \ can \ only \ see \ two \ possibilities- \ either \ grunt \ it \ out \ with \ numerical \ integration \ or \ use \ a \ calculator.\)
\(\displaystyle Note: \ I 've\ set \ up \ the \ integrals \ for \ you, \ now \ the \ ball \ is \ thrown \ in \ your \ lap.\)
\(\displaystyle Note: \ I 've\ set \ up \ the \ integrals \ for \ you, \ now \ the \ ball \ is \ thrown \ in \ your \ lap.\)