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April 3rd, 2017, 07:35 AM   #1
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Double Integrals

Can someone set this integral up for me given: find the volume of the solid formed by f(x,y)= x+y over the region defined by z=0 y=y=x^2, y=1
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April 3rd, 2017, 09:25 AM   #2
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I presume you mean the region below z= f(x,y)= x+ y, above the region in the xy-plane bounded by y= x^2 and y= 1. The simplest thing to do is to take x going from -1 to 1 (y= 1 crosses y= x^2 at (-1, 1) and (1, 1)). For each x, y goes from x^2 up to 1.

The volume is given by $\displaystyle \int_{-1}^1\int_{x^2}^1 (x+ y)dy dx$.

Last edited by skipjack; April 4th, 2017 at 07:29 AM.
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