# Iterated Integral

by shards5
Tags: integral, iterated
 P: 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.
 PF Patron P: 1,132 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.
 PF Patron P: 1,132
P: 38

## Iterated Integral

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

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