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Dec16-07, 04:47 PM
P: 167
I'm confused here.. My definite integral doesn't match by Riemman Sum... and it should right? I think that I have not integrated correctly. Can someone help me spot the problem? Thanks.

Find the Area of the region bounded by:
[tex]f(x)=5-x^2[/tex] , [-2, 1]

Using the Riemma Sum idea (limit of the sum of rectangles as the number of rectangles approaches infinity), I got 12 units^2 as my area, which is correct.

However, using definite integrals and the Fundamental Theorem of Calculus, I get:

[tex]\int_{-2}^{1} (5-x^2)dx}[/tex]

[tex]=-\frac{x^3}{3}\biggl] ^{1}_{-2}[/tex]

Which equals -3 ???
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