- #1
ramb
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1. Homework Statement [/b]
Use the transformation that takes the unit square to a triangle to compute the integral
[tex]\int\int_{B}2x+3y dA[/tex]
Where B is a triangular region with vertices (0,0), (5,2), and (3,4).
What I did was I drew the region on an xy plane, I split the triangle up into two triangles and found my limits of integration by drawing the lines made by connecting the vertices. Because I split the triangle up into two, I needed to add two separate double integrals.
This is what I got.
[tex]\int_{x=0}^{x=3}\int_{y=5x/2}^{y=4x/2}(2x+3y) dydx + \int_{x=3}^{x=5}\int_{y=5x/2}^{y=-x+7}(2x+3y) dydx[/tex]
With the first integral I got
[tex]\dfrac{-651}{8}[/tex]
for the second integral i got
[tex]\dfrac{-4739}{12}[/tex]
I figured that if I add both of them together I would get the volume underneath that region (the whole thing), but the number I got, [tex]\frac{11431}{24}[/tex] seems to large.
I also don't think I'm doing it the method wanted.
Can anyone please direct me where to go from here, I'm somewhat lost.
Thank you
Use the transformation that takes the unit square to a triangle to compute the integral
[tex]\int\int_{B}2x+3y dA[/tex]
Where B is a triangular region with vertices (0,0), (5,2), and (3,4).
The Attempt at a Solution
What I did was I drew the region on an xy plane, I split the triangle up into two triangles and found my limits of integration by drawing the lines made by connecting the vertices. Because I split the triangle up into two, I needed to add two separate double integrals.
This is what I got.
[tex]\int_{x=0}^{x=3}\int_{y=5x/2}^{y=4x/2}(2x+3y) dydx + \int_{x=3}^{x=5}\int_{y=5x/2}^{y=-x+7}(2x+3y) dydx[/tex]
With the first integral I got
[tex]\dfrac{-651}{8}[/tex]
for the second integral i got
[tex]\dfrac{-4739}{12}[/tex]
I figured that if I add both of them together I would get the volume underneath that region (the whole thing), but the number I got, [tex]\frac{11431}{24}[/tex] seems to large.
I also don't think I'm doing it the method wanted.
Can anyone please direct me where to go from here, I'm somewhat lost.
Thank you