Don't definite Integrals find area?
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 ???
|