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

1. modphysnoob

you integrate

2. electrokid

@modphysnoob haha thats no help

3. 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

4. goformit100

Use To Integrate

5. modphysnoob

this is approximation

6. modphysnoob

I will draw a picture and explain this

7. modphysnoob

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

8. modphysnoob

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

9. modphysnoob

see the difference?

10. MoonlitFate

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

11. modphysnoob

right, but to be more precise in left hand approximation, the left side touch the curves, in right hand approx, the right side does

12. 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.

13. MoonlitFate

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

14. modphysnoob

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

15. MoonlitFate

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

16. modphysnoob

right,

17. modphysnoob

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

18. modphysnoob

so each rectangle is 1/2 wide

19. MoonlitFate

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

20. modphysnoob

|dw:1364088406811:dw|

21. 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?

22. modphysnoob

yes

23. 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. :/

24. modphysnoob

sigma just mean sum |dw:1364090915002:dw|

25. MoonlitFate

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

26. MoonlitFate

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

27. modphysnoob

yep, that's all there is to it

28. 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!

29. modphysnoob

I assume you are in calculus 2

30. MoonlitFate

Calculus I.

31. modphysnoob

if you want I can do example for you

32. MoonlitFate

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

33. modphysnoob

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

34. modphysnoob

|dw:1364157838998:dw|

35. modphysnoob

so we wanna approximate the area under the curve using 2 rectangle so first rectangle would be from 0 to 1 1 to 2

36. MoonlitFate

Okay.

37. modphysnoob

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

38. MoonlitFate

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

39. modphysnoob

well, there you have it , left and right approximation

40. modphysnoob

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