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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.

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,

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

Theorem 4 states that:

"If

[tex]\int[/tex][tex]\stackrel{b}{a}[/tex]

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

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..

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,

*n*is above Sigma and*i = 1*is under it.**1. Homework Statement**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. Homework Equations**Theorem 4 states that:

"If

*f*is 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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