E-AR02 · An equal-area cut
The curves \(y=8x-2x^2\) and \(y=2x\) enclose a region R.
Find their intersection coordinates.
Find the exact area of R.
Show that \(\displaystyle x=\frac32\) divides R into equal areas, and explain why there is no other vertical equal-area cut inside R.
Complete-answer checking, worked solutions and indicative written criteria.
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