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