does anyone know how to use "Limit of Sums" to find an area??

Question

anonymous · Answer

do you have a specific question?

anonymous · Answer

https://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/riemann-sums/e/the-definite-integral-as-the-limit-of-a-riemann-sum

anonymous · Answer

Find the area of f(x)=x^2, bounded by [1,7]

misty1212 · Answer

HI!!
you mean compute the riemann sum?

misty1212 · Answer

if you do, we can do it, but it is really going to take a while, and pretty much suck

anonymous · Answer

I missed a class, so I'm not exactly sure. I assumed it would suck though...

misty1212 · Answer

first off the answer is easy
the anti derivative of $x^2$ is $\frac{x^3}{3}$ so the answer is 
$$\frac{7^3}{3}-\frac{1}{3}$$

misty1212 · Answer

but if you want to compute a riemann sum you have to take the limit of a sum
first the interval from 1 to 7 has length 6, so all the $n$ little rectangles will have base $\frac{6}{n}$

misty1212 · Answer

then you have to write what those divisions are 
first is $x_0=1$ the next one is $x_1+\frac{6}{n}$
then $x_2=1+\frac{12}{n}$ and in general $$x_k=1+\frac{6k}{n}$$ did i lose  you yet?

anonymous · Answer

umm, go on lol. I think that makes sense

anonymous · Answer

We are supposed to use 10, 20, 40, and 80 midpoint rectangles. 
so I got, .6, .3, .15, and .075

misty1212 · Answer

oh lord in that case you are on  your own
use a spreadsheet or something

anonymous · Answer

Yeah.. I know how to do like 3 or 4, but 40 and 80 would be ridiculous. I figured I was missing something

triciaal · Answer

|dw:1423457084022:dw|