How to find the area under a curve?

- MoonlitFate

How to find the area under a curve?

- jamiebookeater

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- anonymous

you integrate

- anonymous

@modphysnoob haha thats no help

- 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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## More answers

- goformit100

Use To Integrate

- anonymous

this is approximation

- anonymous

I will draw a picture and explain this

- anonymous

|dw:1364087469983:dw|
this is left hand approximation

- anonymous

|dw:1364087569386:dw|
this is right hand approximation

- anonymous

see the difference?

- MoonlitFate

One is above the curve, and one is below it, to put it simply. :)

- 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

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

Err, left approximation, not right in that first sentence.

- anonymous

yes, right, so as you said, in left hand over approximate, right hand under approximate

- MoonlitFate

All right. I know that you have divide the interval into subintervals. Since it's 6 rectangles, that means 6 subintervals, right?

- anonymous

right,

- anonymous

so from 2 to 5
5- 2
-------------------
6
3/6
1/2

- anonymous

so each rectangle is 1/2 wide

- MoonlitFate

Yeah, I was getting there! So, I understand that part. :)

- anonymous

|dw:1364088406811:dw|

- 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

yes

- 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

sigma just mean sum
|dw:1364090915002:dw|

- MoonlitFate

Yes, I know that much. It's just figuring out the pattern is where I have trouble.

- MoonlitFate

I mean, I know that's going to be all the areas of rectangles added together.

- anonymous

yep, that's all there is to it

- 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

I assume you are in calculus 2

- MoonlitFate

Calculus I.

- anonymous

if you want I can do example for you

- MoonlitFate

@modphysnoob - I know this a late reply, but by all means go for it, if you don't mind. :)

- anonymous

so let's do a parabola
f(x)= x^2
|dw:1364157776078:dw|

- anonymous

|dw:1364157838998:dw|

- 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

Okay.

- 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

Okay, I follow you so far. :) Sorry for the delay in answering; internet problems.

- anonymous

well, there you have it , left and right approximation

- anonymous

you will learn trapizoid approximation which is average between left and right hand

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