Integral help...

[SirDeity]

I'm new to integrals and am stuck on my first problem. The problem asks what the limit as n goes to infinity is in the problem: n over the funky E symbol (sorry, I don't remember its name) and i=1 under it with (2xsubi-7)/n to the right of it. The problem also says that the interval [0,3] is partitioned into n equal subintervals. I don't know how to put calculus symbols on here so I hope someone can understand what I'm asking...

I thought the solution was as simple as integrating or doing the opposite of taking the derivative. So I asked myself what function must exist for f'(x)=2x-7 to be its derivative? Fortunately it seems simple enough... the derivative of f(x)=X^2 -7x is 2x-7, right? Then I tried the following:

[(3)^2-7(3)]-[(0)^2-7(0)] = [-12]-[0] = -12

But -12 isn't the answer and I don't know what I'm doing wrong... can anyone please assist me? Thank you.


Thanks.

 

[tkhunny]

It's an upper case SIGMA. It stands for summation of a defined sequence of values. Finite summation is not the same thing as integration. They are related.

 

[-GC-Phoenix]

im just thinking, if the equation is (2x-7)/n, and the problem is asking what the limit is as n goes to infinity, then the answer is simply 0. Because if you are dividing any number by a very large number, it gets very close to 0, and will continue to go to 0 the closer that n gets to infinity.

thanks what Im thinking

 

[stapel]

...the limit as n goes to infinity is in the problem: n over the funky E symbol (sorry, I don't remember its name) and i=1 under it with (2xsubi-7)/n to the right of it.

Do you mean the following?

. . . . .\(\displaystyle \L \begin{array}{c}\mbox{limit}\\n\rightarrow\infty\end{array}\, \sum_{i=1}^n\, \frac{2x_i\,-\,7}{n}\)

Note: The above can also be written as:

. . . . .lim [n->infty] [ sum [i=1,n] [ (2x_i - 7) / n ] ]

The problem also says that the interval [0,3] is partitioned into n equal subintervals.

I'm sorry, but I'm not seeing how this relates...?

Eliz.

 

[tkhunny]

im just thinking, if the equation is (2x-7)/n, and the problem is asking what the limit is as n goes to infinity, then the answer is simply 0. Because if you are dividing any number by a very large number, it gets very close to 0, and will continue to go to 0 the closer that n gets to infinity.

thanks what Im thinking

Good try. You totally get credit for thinking about what you are doing. Nevertheless, you have come to an incorret conclusion. It is sometimes a struggle to jump from finite to infinite. Watch:

1

Cut it in half and add them both.

1/2 + 1/2 = 1

Cut those in half and add them up.

1/4 + 1/4 + 1/4 + 1/4 = 1

See how it always adds to the same thing?

Do it again.

1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 = 1

Still 1!

If we cut it up into 10 million pieces, each piece will be very small, but it will still add to 1. How about 200 billion pieces? Still 1. What is the limit of this process as the number of pieces increases without bound? Why would it get to zero as you have suggested? Still 1.

Infinite things do not always act like finite things, but with a little care they can be motivated in some logical manner.