Iterated Integral

shards5

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
6y²+12y³+6y⁴+5+10y+5y²-6y+12y³-6y⁴-5+10y-5y²
Most of the stuff cancels out giving me
12y³+12y³+10y+10y
which simplifies to
[tex] \int^{1}_{0} 24y^3+20y dy [/tex]
and after integration I get
6y⁴+10y²
and after plugging in my numbers I get
6+10 = 16 which is wrong. I am not sure where I screwed up.

jhae2.718

Don't use sup in LaTeX; exponents are indicated by ^, with braces {} if the exponent is more than one character long.

I only briefly looked at your work, but you might want to check your substitution of limits in the first integrand.

jhae2.718

<double post>

shards5

You, were right! I screwed up by substituting the limits into the y instead of x by mistake. Thanks a lot.