Need Help with Integral Proof? Get Step-by-Step Explanation | 4/3 Answer

[syphonation]

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, n is above Sigma and i = 1 is under it.

Homework Statement

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

$$\int$$$$\stackrel{2}{0}$$ (2-x^2)dx

Homework Equations

Theorem 4 states that:

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

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

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

The Attempt at a Solution

The answer is 4/3.

$$\Delta$$x = (2-0)/n = 2/n

x sub i = a + i$$\Delta$$x = 0 + (2/n)i

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

 

[quasar987]

Alright, so what do you get when you put those values into the formula of theorem 4?

Click on this to see the code i used:

$$\int_a^bf(x)dx = \lim_{n\rightarrow +\infty}\sum_{i=1}^nf(x_i)\Delta x$$

 

[syphonation]

Alright, I finally figured it out. Now I feel like an idiot.

Thanks for the Tex code.