The discussion centers on the feasibility of changing the order of integration in double integrals, specifically regarding the volume calculation of a region defined by the cylinder x² + z² = 1 and the planes y=0, z=0, and x=y. It is established that y can be treated as the independent variable while x is the dependent variable, allowing for a valid transformation of the integral. The participants emphasize the importance of understanding the geometric implications of the variables involved in the volume calculation.
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Jazzyrohan said: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?