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chemojoe

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Say that I cite a geometric reason why the rev. volume/area under a curve is so rather than the expanding an integral. If I write the integral wrong eg instead of π∫[f(x)]^2dx I do π∫f(x)dx for a volume but my geometric reasoning is right (eg the shape is a hemisphere with radius 1, therefore volume is 2pi/3), should I expect to lose a mark? Is this a strange situation?

Also, for integrals involving absolute values (linear eg y=2-|x|), I find that raising powers is finicky, so is it fine if i explain that I can break the area into triangles, mirroring across the y-axis? do you even need an explanation if its clear enough? thx
 

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