Doug C. answered • 02/13/17

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Hi Pat,

In order to find the points of intersection of the line with the parabola, substitute x=7-y for x into the equation of the parabola. You will find that the points of intersection are located at (7,0) and (0,7).

Sketch a graph then realize that the height of a typical shell can be represented by 16 - (y-3)

^{2}- (7-y) (right x - left x)Take a look here: https://www.desmos.com/calculator/k9u7rg7rty

The integral has been set up there, an answer supplied. See if you can complete the work in between.