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I am wondering ifmy curves look like

$y=9-x^2, z=x^2-3x$

for area between curves, why isit just

$\int^{3}_{-3/2}(9-x^2)-(x^2-3x) dx$

I don’t care if there’s a change of sign?

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Your integrand gives the distance between the two functions at $x$ always (top point - bottom point). So it's fine... –  David Mitra Nov 17 '11 at 13:41
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up vote 0 down vote accepted

Think what would happen if you added a constant, say $5$, to both $y$ and $z$.

Alternatively, imagine the area made up of rectangles with infinitesimal width, calculate the lengths of those rectangles in terms of $y$ and $z$, and check whether anything changes about that when one of the functions changes sign.

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