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lLovePhysics
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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:
f(x)=5-x^2 , [-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:
\int_{-2}^{1} (5-x^2)dx}
=-\frac{x^3}{3}\biggl] ^{1}_{-2}
Which equals -3 ?
Find the Area of the region bounded by:
f(x)=5-x^2 , [-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:
\int_{-2}^{1} (5-x^2)dx}
=-\frac{x^3}{3}\biggl] ^{1}_{-2}
Which equals -3 ?