Question

I have no idea how to set the bounds of integration. The 2 functions that make up this shape are y(y-6)+1 and [cos(pi*y)/6]^2

Image transcriptions

Here's a region R plotted in the xy-plane. Clear [y]; Rplot = ParametricPlot[{{y (y - 6) + 1, y}, {Cos[ (Pi y)/6]^2, y}}, {y, 0, 6}, PlotStyle -> {{Red, Thickness [0. 01]}}, AxesLabel -> {"x", "y"}, Epilog -> Text["R", {-4, 3}]] 5 TITTT 4 R 3 2 -8 X -6 -4 -2 Go with f[x,y] = y-x+3 and calculate S S, flex, ylaxdy by the method of least labor on your part.

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