(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Evaluate the iterated integral I = [tex] \int^{1}_{0}\int^{1+y}_{1-y} (6y^2+ 10x) dxdy [/tex]

2. Relevant equations

. . . ?

3. The attempt at a solution

Integrate with respect to x gives me the following equation.

[tex] \int^{1}_{0} 6xy^2 + 5x^2 dy [/tex]

I plug in y+1 and y-1 into x and get the following

6y^{2}+12y^{3}+6y^{4}+5+10y+5y^{2}-6y+12y^{3}-6y^{4}-5+10y-5y^{2}

Most of the stuff cancels out giving me

12y^{3}+12y^{3}+10y+10y

which simplifies to

[tex] \int^{1}_{0} 24y^3+20y dy [/tex]

and after integration I get

6y^{4}+10y^{2}

and after plugging in my numbers I get

6+10 = 16 which is wrong. I am not sure where I screwed up.

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# Iterated Integral

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