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Iterated Integral

by shards5
Tags: integral, iterated
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shards5
#1
Mar18-11, 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}_{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.
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jhae2.718
#2
Mar18-11, 04:40 PM
PF Gold
jhae2.718's Avatar
P: 1,153
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
#3
Mar18-11, 04:40 PM
PF Gold
jhae2.718's Avatar
P: 1,153
<double post>

shards5
#4
Mar18-11, 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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