Shaded Region, Area between Curves and X-axis

SDF

Apr 2014
75
3
Canada
Is there a formal way to approach finding the area of the shaded region in this diagram? From the examples it looks like they're flipping the sign of the entire integral. Both of them, actually.

a1.png

Btw, the answer is: \(\displaystyle \int_{-\sqrt{10}}^{-1}(-x^2+10)dx+\int_{-1}^{0}-9xdx\)
 
Last edited by a moderator:
Dec 2013
2,002
757
Colombia
Yes, because we are asked for the area, which implies a positive number. But the integrals of the functions will be negative because the area is beneath the \(\displaystyle x\)-axis.
 
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SDF

Apr 2014
75
3
Canada
Yes, because we are asked for the area, which implies a positive number. But the integrals of the functions will be negative because the area is beneath the \(\displaystyle x\)-axis.
I guess the terminology I was after was "signed area". Lots of information available now. Thanks.