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seanc12
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Homework Statement
Solve the following Double Intergral, and show the answer is the same, regardless of which order you integrate.
The integral is between the boundaries [tex]y=x[/tex] and [tex]y=x^2[/tex]
Homework Equations
[tex]\int[/tex][tex]\int_R (x^2 + 2y)dxdy[/tex]
The Attempt at a Solution
So first of all i integrated with repsect to y first
[tex]\int_0^1 dx[/tex] [tex]\int^{x}_{x^2} (x^2 + 2y)dy[/tex]
[tex]\int_0^1 dx [yx^2+y^2]^x^2_x[/tex]
[tex]\int_0^1 dx (x^3 + x^2 - 2x^4)[/tex]
which give me an answer of
[tex]\frac{11}{60}[/tex]Then, with respect to x first I get:
[tex]\int_0^1 dy [/tex] [tex]\int_{\sqrt{y}}^y dx (x^2 + 2y)[/tex]
[tex]\int_0^1 dy [\frac{x^3}{3} + 2xy ]^{y}_{\sqrt{y}}[/tex]
[tex]\int_0^1 dy(\frac{y^3}{3} + 2y^2 - \frac{\sqrt{y}^3}{3} - \frac{2\sqrt{y}y}{3})[/tex]
This leads me to an answer different to what I got from differenciating with repect to y first.
Can someone please enlighten me with what I am doing wrong.
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