Question: You have found the volume under a given surface (such as x3y or x4y43) over a given region. But what about the volume between two

You have found the volume under a given surface (such as x3y or x4y43) over a given region. But what about the volume between two surfaces? For this, you have to find the region of integration in the xy-plane, and then set up the limits of integration.(a) Consider the surfaces z=-(x2-y)(y-x-2)-x and z=4(x2-y)(y-x-2)-x, pieces of which are shown to the right. Find the curves in the xy-plane that are the shadows of the intersection curves of these surfaces. Sketch the curves in the xy-plane and shade the region between them, which is our region of integration.(b) Write a double integral to find the volume of the solid that is enclosed between the surfaces, and then compute its value (it is tedious, so you may use a calculator).

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