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Don't definite Integrals find area?

  1. Dec 16, 2007 #1
    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 ???
     
  2. jcsd
  3. Dec 16, 2007 #2
    5x - 1\3 * x^3
     
  4. Dec 16, 2007 #3
    Noooo.. I can't believe I made another stupid mistake!! Thanks Roco
     
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