January 24, 2017

Homework Help: Calculus

Posted by Sean on Monday, May 30, 2011 at 10:33pm.

Evaluate the definite integral from [0,4] 4x^2 dx, by using its definition as a limit of approximating sums.

First, I solve analytically so I know the answer I am trying to reach: 4/3 * x^3 over [0,4] = 4/3 * 4^3 = 256/3

Now, by approximating sums, I can get:

256 * lim(n -> infinity) of sum(j=0 to n-1) of j^2/n^3

I can use the computer to solve this and I reach the correct answer. In Mathematica Alpha notation: 256 * lim sum j^2/n^3, j=0..n as n -> infinity

How do I solve that limit by hand? Or is there a better way to solve the original problem?

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