I have posted a problem from my book below. I am having trouble with a homework problem similar to this one and can't, for the life of me, figure it out. The back of the book says the ansewer to this problem is 4/3. I can't figure how they're getting that. I've tried everything I can think of, and I'm not even close.(adsbygoogle = window.adsbygoogle || []).push({});

Could someone explain how to solve this problem? I hate to post it with no solution attempt, but I am lost.

Please excuse the sorry attempt at using LaTex..I wrote it out the best I could. Obviously,nis above Sigma andi = 1is under it.

1. The problem statement, all variables and given/known data

Use the form of the defenition of the integral given in Theorem 4 to evaluate the integral.

[tex]\int[/tex][tex]\stackrel{2}{0}[/tex] (2-x^2)dx

2. Relevant equations

Theorem 4 states that:

"Iffis integrable on [a,b], then the following is true:

[tex]\int[/tex][tex]\stackrel{b}{a}[/tex]f(x)dx= lim as n --> [tex]\infty[/tex] [tex]\sum[/tex][tex]\stackrel{n}{i=1}[/tex]f(x sub i)[tex]\Delta[/tex]x

where [tex]\Delta[/tex]x = (b-a)/n and x sub i = a + i[tex]\Delta[/tex]x

3. The attempt at a solution

The answer is 4/3.

[tex]\Delta[/tex]x = (2-0)/n = 2/n

x sub i = a + i[tex]\Delta[/tex]x = 0 + (2/n)i

That's all I have that I know is right..

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# Homework Help: Help with Integral Proof

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