Double Integral problem (E^x^3)

Lucas Mayr
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Relevant equations

cd98f00b204e9800998ecf8427eo4ltj0je2q&f=HBQTQYZYGY4TQM3BGZRTSNJRHEYDCM3CMM2GMNRYGMYDIN3FGFQQaaaa.gif


The Attempt at a Solution


i've tried changing the integration values from dxdy to dydx, but without success.
i can't seem to get the same result after i change the ranges
tried to change to 0<x<1 , x^2 < y <1
some light would be appreciated
 
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Lucas Mayr said:
Relevant equations

cd98f00b204e9800998ecf8427eo4ltj0je2q&f=HBQTQYZYGY4TQM3BGZRTSNJRHEYDCM3CMM2GMNRYGMYDIN3FGFQQaaaa.gif


The Attempt at a Solution


i've tried changing the integration values from dxdy to dydx, but without success.
i can't seem to get the same result after i change the ranges
tried to change to 0<x<1 , x^2 < y <1
some light would be appreciated

Did you draw a sketch of the region? I think 0 < y < x^2.
 
i just did a re-sketch of the region and i was looking at it the wrong way, the range is 0<y<x^2 like you said.
such a silly mistake >.<
thanks for the help
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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