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MoonlitFate
How to find the area under a curve?
@modphysnoob haha thats no help
*Use the left and right endpoints and the given number of rectangles to find two approximations of the area of the region between the graph of the function and the x-axis over the given interval. g(x) = 2x^2-x-1, [2,5], 6 rectangles
this is approximation
I will draw a picture and explain this
|dw:1364087469983:dw| this is left hand approximation
|dw:1364087569386:dw| this is right hand approximation
see the difference?
One is above the curve, and one is below it, to put it simply. :)
right, but to be more precise in left hand approximation, the left side touch the curves, in right hand approx, the right side does
You mean that all of the left endpoints of each rectangle touch the curve for the right approximation and the same for the left? Just making sure that I follow.
Err, left approximation, not right in that first sentence.
yes, right, so as you said, in left hand over approximate, right hand under approximate
All right. I know that you have divide the interval into subintervals. Since it's 6 rectangles, that means 6 subintervals, right?
so from 2 to 5 5- 2 ------------------- 6 3/6 1/2
so each rectangle is 1/2 wide
Yeah, I was getting there! So, I understand that part. :)
|dw:1364088406811:dw|
So, for left hand approximation, I would use the left end points for each subinterval. So, the length of each rectangle would be g(x) evaluated at each left endpoint of that subinterval?
Okay. This is starting to make a little bit of sense, :) One big thing that confuses me is the Sigma notation that is adding in with this. :/
sigma just mean sum |dw:1364090915002:dw|
Yes, I know that much. It's just figuring out the pattern is where I have trouble.
I mean, I know that's going to be all the areas of rectangles added together.
yep, that's all there is to it
I'll see if I can find some videos to help, too. :) Easier to grasp things when you see examples being worked out. But, at least, I understand a bit more! I can do this!
I assume you are in calculus 2
if you want I can do example for you
@modphysnoob - I know this a late reply, but by all means go for it, if you don't mind. :)
so let's do a parabola f(x)= x^2 |dw:1364157776078:dw|
|dw:1364157838998:dw|
so we wanna approximate the area under the curve using 2 rectangle so first rectangle would be from 0 to 1 1 to 2
0 1 2 in left approximation we will take 2 rectangles with height at 0 and 1 and multiply by width =1 f(0)*1+f(1)*1 in right approoximation , we take height at 1 and 2 f(1)*1+f(2)*1
Okay, I follow you so far. :) Sorry for the delay in answering; internet problems.
well, there you have it , left and right approximation
you will learn trapizoid approximation which is average between left and right hand