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Paladinen [302]
3 years ago
11

Answer if you know

Mathematics
1 answer:
Arlecino [84]3 years ago
8 0
I've attached a plot of one such cross-section (orange) over the region in the x-y plane (blue), including the bounding curves (red). (I've set y=1.25 for this example.)

The length of each cross section (the side lying in the base) has length determined by the horizontal distance x between the y-axis x=0 and the curve y=\sqrt x. In terms of y, this distance is x=y^2. The height of each cross section is twice the value of y, so the area of each rectangular cross section should be 2y^3.

This means the volume would be given by the integral

\displaystyle\int_0^22y^3\,\mathrm dy
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