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MoonlitFate
 2 years ago
How to find the area under a curve?
MoonlitFate
 2 years ago
How to find the area under a curve?

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electrokid
 2 years ago
Best ResponseYou've already chosen the best response.0@modphysnoob haha thats no help

MoonlitFate
 2 years ago
Best ResponseYou've already chosen the best response.0*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 xaxis over the given interval. g(x) = 2x^2x1, [2,5], 6 rectangles

modphysnoob
 2 years ago
Best ResponseYou've already chosen the best response.2this is approximation

modphysnoob
 2 years ago
Best ResponseYou've already chosen the best response.2I will draw a picture and explain this

modphysnoob
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1364087469983:dw this is left hand approximation

modphysnoob
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1364087569386:dw this is right hand approximation

modphysnoob
 2 years ago
Best ResponseYou've already chosen the best response.2see the difference?

MoonlitFate
 2 years ago
Best ResponseYou've already chosen the best response.0One is above the curve, and one is below it, to put it simply. :)

modphysnoob
 2 years ago
Best ResponseYou've already chosen the best response.2right, but to be more precise in left hand approximation, the left side touch the curves, in right hand approx, the right side does

MoonlitFate
 2 years ago
Best ResponseYou've already chosen the best response.0You 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
 2 years ago
Best ResponseYou've already chosen the best response.0Err, left approximation, not right in that first sentence.

modphysnoob
 2 years ago
Best ResponseYou've already chosen the best response.2yes, right, so as you said, in left hand over approximate, right hand under approximate

MoonlitFate
 2 years ago
Best ResponseYou've already chosen the best response.0All right. I know that you have divide the interval into subintervals. Since it's 6 rectangles, that means 6 subintervals, right?

modphysnoob
 2 years ago
Best ResponseYou've already chosen the best response.2so from 2 to 5 5 2  6 3/6 1/2

modphysnoob
 2 years ago
Best ResponseYou've already chosen the best response.2so each rectangle is 1/2 wide

MoonlitFate
 2 years ago
Best ResponseYou've already chosen the best response.0Yeah, I was getting there! So, I understand that part. :)

modphysnoob
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1364088406811:dw

MoonlitFate
 2 years ago
Best ResponseYou've already chosen the best response.0So, 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?

MoonlitFate
 2 years ago
Best ResponseYou've already chosen the best response.0Okay. 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. :/

modphysnoob
 2 years ago
Best ResponseYou've already chosen the best response.2sigma just mean sum dw:1364090915002:dw

MoonlitFate
 2 years ago
Best ResponseYou've already chosen the best response.0Yes, I know that much. It's just figuring out the pattern is where I have trouble.

MoonlitFate
 2 years ago
Best ResponseYou've already chosen the best response.0I mean, I know that's going to be all the areas of rectangles added together.

modphysnoob
 2 years ago
Best ResponseYou've already chosen the best response.2yep, that's all there is to it

MoonlitFate
 2 years ago
Best ResponseYou've already chosen the best response.0I'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!

modphysnoob
 2 years ago
Best ResponseYou've already chosen the best response.2I assume you are in calculus 2

modphysnoob
 2 years ago
Best ResponseYou've already chosen the best response.2if you want I can do example for you

MoonlitFate
 2 years ago
Best ResponseYou've already chosen the best response.0@modphysnoob  I know this a late reply, but by all means go for it, if you don't mind. :)

modphysnoob
 2 years ago
Best ResponseYou've already chosen the best response.2so let's do a parabola f(x)= x^2 dw:1364157776078:dw

modphysnoob
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1364157838998:dw

modphysnoob
 2 years ago
Best ResponseYou've already chosen the best response.2so we wanna approximate the area under the curve using 2 rectangle so first rectangle would be from 0 to 1 1 to 2

modphysnoob
 2 years ago
Best ResponseYou've already chosen the best response.20 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
 2 years ago
Best ResponseYou've already chosen the best response.0Okay, I follow you so far. :) Sorry for the delay in answering; internet problems.

modphysnoob
 2 years ago
Best ResponseYou've already chosen the best response.2well, there you have it , left and right approximation

modphysnoob
 2 years ago
Best ResponseYou've already chosen the best response.2you will learn trapizoid approximation which is average between left and right hand
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