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)=5x^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} (5x^2)dx}[/tex]
[tex]=\frac{x^3}{3}\biggl] ^{1}_{2}[/tex]
Which equals 3 ???
