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[GaimeGuy]

The circles x² + y² = 2 and (x-1)² + y² = 1 intersect at the points (1,1) and (1, -1) Let R be the shaded region in the first quadrant bounded by the two circles and the x-axis

Set up an expression involving one or more integrals with respect to y that represent the area of R.

now, I was able to set up two integrals using dx slices, but I just can't figure the dy slices out. Help

 

[Macam]

It helps to draw a picture. The first circle is centered at the origin with a radius of the square root of 2; the second circle is centered at x=1 with a radius of 1. Since the square root of 2 is just larger than 1, the graph looks somewhat akin to a Venn diagram (or the MasterCard logo), with the region enclosed by both circles and the x-axis going from 0 to square root of 2 along the x-axis and from 0 to 1 (since they interset at (1,1) and that's in the first quadrant). So from that info alone you should be able to determine the limits of your double integral, depending on whether you need it to be in rectangular coordinates or, more likely, in polar coordinates.

 

[GaimeGuy]

I actually have the picture. I just can't figure out what the fuck to put in for the integrals. I know that one of them has to be an integral, from y = 0 to y=1 , of
√(2-y²)dy, but I can't figure out the second one.

I thought it was an integral from y = 0 to y=1 of √[1-(y²)] + 1 dy, but it doesn't come out with the same area as I calculated using dx slices. and I am SURE that I got the dx slices right. I even checked with my teacher. But I can't figure out what's wrong with my integrals using y.