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Iterated Integral 
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#1
Mar1811, 04:25 PM

P: 38

1. The problem statement, all variables and given/known data
Evaluate the iterated integral I = [tex] \int^{1}_{0}\int^{1+y}_{1y} (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 y1 into x and get the following 6y^{2}+12y^{3}+6y^{4}+5+10y+5y^{2}6y+12y^{3}6y^{4}5+10y5y^{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. 


#2
Mar1811, 04:40 PM

PF Gold
P: 1,160

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. 


#4
Mar1811, 05:27 PM

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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