Find volume of body bounded by surfaces

[JKroo]

Find volume of body bounded by surfaces:
z=2y, z=0, y=x^2, y=x

 

[Deleted member 4993]

Find volume of body bounded by surfaces: z=2y, z=0, y=x^2, y=x

To do these types of problems, you should first try to sketch the problem and decide on a the method (washer or disk) and establish limits of integration. Have you done that?

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this assignment.

 

[HallsofIvy]

z= 0 is the xy-plane, z= 2y is a plane at an angle above the xy-plane. \(\displaystyle y= x^2\) and y= x are perpendicular to the xy-plane.

y= x^2 is a parabola and y= x is a line that intersects that parabola at (0, 0) and at (1, 1). To find the area of the figure bounded by them you would integrate \(\displaystyle \int_0^1\int_{x^2}^x dydx\). To find the volume of the region above that area, do \(\displaystyle \int_0^2\int_{x^2}^x 2y dydx\).