Change of order in double integrals

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In the question given below, can we change the order of integral so that y can be the independent variable and x be the dependent one?


The cylinder x^2 + z^2 = 1 is cut by the planes y=0,z=0 and x=y.Find the volume of the region in the first octant.


This may look like a homework question but it's not.I just want to know whether what I have asked is possible and if yes,then how so?
 

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PeroK
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In the question given below, can we change the order of integral so that y can be the independent variable and x be the dependent one?


The cylinder x^2 + z^2 = 1 is cut by the planes y=0,z=0 and x=y.Find the volume of the region in the first octant.


This may look like a homework question but it's not.I just want to know whether what I have asked is possible and if yes,then how so?
Why is ##x## special? In which way are ##x, y## and ##z## fundamentally different when it comes to the volume of a solid?
 

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