# Iterated Integral

1. ### shards5

38
1. The problem statement, all variables and given/known data
Evaluate the iterated integral I = $$\int^{1}_{0}\int^{1+y}_{1-y} (6y^2+ 10x) dxdy$$

2. Relevant equations

. . . ?

3. The attempt at a solution
Integrate with respect to x gives me the following equation.
$$\int^{1}_{0} 6xy^2 + 5x^2 dy$$
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
$$\int^{1}_{0} 24y^3+20y dy$$
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.

2. ### jhae2.718

1,152
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.

3. ### jhae2.718

1,152
<double post>

4. ### shards5

38
You, were right! I screwed up by substituting the limits into the y instead of x by mistake. Thanks a lot.