MoonlitFate
  • MoonlitFate
How to find the area under a curve?
Calculus1
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
you integrate
anonymous
  • anonymous
@modphysnoob haha thats no help
MoonlitFate
  • MoonlitFate
*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

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goformit100
  • goformit100
Use To Integrate
anonymous
  • anonymous
this is approximation
anonymous
  • anonymous
I will draw a picture and explain this
anonymous
  • anonymous
|dw:1364087469983:dw| this is left hand approximation
anonymous
  • anonymous
|dw:1364087569386:dw| this is right hand approximation
anonymous
  • anonymous
see the difference?
MoonlitFate
  • MoonlitFate
One is above the curve, and one is below it, to put it simply. :)
anonymous
  • anonymous
right, but to be more precise in left hand approximation, the left side touch the curves, in right hand approx, the right side does
MoonlitFate
  • MoonlitFate
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.
MoonlitFate
  • MoonlitFate
Err, left approximation, not right in that first sentence.
anonymous
  • anonymous
yes, right, so as you said, in left hand over approximate, right hand under approximate
MoonlitFate
  • MoonlitFate
All right. I know that you have divide the interval into subintervals. Since it's 6 rectangles, that means 6 subintervals, right?
anonymous
  • anonymous
right,
anonymous
  • anonymous
so from 2 to 5 5- 2 ------------------- 6 3/6 1/2
anonymous
  • anonymous
so each rectangle is 1/2 wide
MoonlitFate
  • MoonlitFate
Yeah, I was getting there! So, I understand that part. :)
anonymous
  • anonymous
|dw:1364088406811:dw|
MoonlitFate
  • MoonlitFate
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?
anonymous
  • anonymous
yes
MoonlitFate
  • MoonlitFate
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. :/
anonymous
  • anonymous
sigma just mean sum |dw:1364090915002:dw|
MoonlitFate
  • MoonlitFate
Yes, I know that much. It's just figuring out the pattern is where I have trouble.
MoonlitFate
  • MoonlitFate
I mean, I know that's going to be all the areas of rectangles added together.
anonymous
  • anonymous
yep, that's all there is to it
MoonlitFate
  • MoonlitFate
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!
anonymous
  • anonymous
I assume you are in calculus 2
MoonlitFate
  • MoonlitFate
Calculus I.
anonymous
  • anonymous
if you want I can do example for you
MoonlitFate
  • MoonlitFate
@modphysnoob - I know this a late reply, but by all means go for it, if you don't mind. :)
anonymous
  • anonymous
so let's do a parabola f(x)= x^2 |dw:1364157776078:dw|
anonymous
  • anonymous
|dw:1364157838998:dw|
anonymous
  • anonymous
so we wanna approximate the area under the curve using 2 rectangle so first rectangle would be from 0 to 1 1 to 2
MoonlitFate
  • MoonlitFate
Okay.
anonymous
  • anonymous
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
MoonlitFate
  • MoonlitFate
Okay, I follow you so far. :) Sorry for the delay in answering; internet problems.
anonymous
  • anonymous
well, there you have it , left and right approximation
anonymous
  • anonymous
you will learn trapizoid approximation which is average between left and right hand

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