37) The Area Under a Curve: approx. the definite intergral
Loading...
Uploader Comments (Lutemann)
All Comments (15)
-
@denissjacenko the indefinite integral of x squared is x cubed over 3 ∫x^2 dx = (x^3)*(1/3) The integral is like the anti derivative. so if you take the derivative of (x^3)*(1/3) you get x^2 now using this integral, evaluate from 1 to 3
this means that you plug in 3 for x into (x^3)*(1/3) and subtract 1 plugged into (x^3)*(1/3). so you have (3^3)*(1/3) - (1^3)*(1/3) = 27/3 - 1/3 = 26/3
-
how did you get 26/3?
-
Good video and you explain it very well, n=4 as partitions are good, n=5 is also well. Do you have more examples of the definite integreals that someone might use in a real life situations? thanks for your time.
-
5 stars yea.. sorry no stars in the rating system anymore
anyway thanks a lot
-
at the end you said twenty three thirds instead of twenty 26 lol.
Great video though, 5 stars
2 years ago 2
-
Thanks
-
you have 4 rectangles between 1 and 3. the bases of these are 1 to x1, x1 to x2, x2 to x3 and x3 to 3 right? so x1 = 1 + delta x. delta x is .5 so x1 = 1.5 then x2 = 1.5 + .5 = 2 and so on
-
why did the roots of the squares increase? i.e x1= 1.5, x2=2, x3=2.5etc...?
- 5:06
40) The Fundamental Theorem of Calculus Explainedby Lutemann34,209 views
- 4:03
38) Mean Value Theorem, Part 1 of 2by Lutemann10,309 views
- 3:09
9) The Definition of the Derivative, Part 1 of 3by Lutemann13,954 views
- 3:03
1) Finding the Limits From a Graph, Part 1 of 2by Lutemann37,200 views
- 3:52
How to Find Approximate Area Using Sigma Notation For Dummiesby fordummies16,190 views
- 1:46
18) Implicit Differentiation, Part 1 (of three parts)by Lutemann12,114 views
- 4:57
33) Optimization (the soup can problem)by Lutemann7,990 views
- 1:21
How to Make a Line Graphby DeeReavis15,236 views
- 4:33
What is Calculus Anyways !!!by thrashmetal814,618 views
- 6:05
3) Limits: An Intuitive Approach, Part 1 of 5by Lutemann8,799 views
- 9:49
4.2 Estimating the Area Under a Curveby rootmath2,536 views
- 5:53
Approximating Area Using Rectanglesby brightstorm218,237 views
- 2:33
35) Related Rates, Part 1 of 2by Lutemann5,936 views
- 5:54
Calculus Documentaryby n00bgankr16,086 views
- 1:32
What is Calculus?by CerebellumCorp103,859 views
- 1:05
13) The Quotient Rule, Part 1 of 2by Lutemann4,334 views
- 9:42
4.3 Exact Area Under a Curve 02by rootmath2,975 views
- 3:17
8) Continuity at a Pointby Lutemann4,708 views
- 4:58
The Fundamental Theorem of Calculusby garybooker2,646 views
- 2:30
Fundamental Theorem of Calculus (part 1 of 3)by calctube8,222 views
I used the fundamental theorem of calculus.
Lutemann 1 year ago
why did you use n=4?? or is it just an arbitrairy choice
thanx for sharing the knowledge
Roelandvinken 3 years ago
It's arbitrary. If you can do it with four then you can do it with three or ten or whatever. Four comes out pretty neat, though.
Lutemann 3 years ago
Nice video, though I'd like to point out that you didn't mention that this particular example is a right-hand Riemman sum, nor did you mention that there are three more types of Riemman sums, two of which give a more accurate area. I think that info would have made the video more helpful. Other than that good work.
dannysaurusrex 3 years ago
You are correct and I show my students the more general approach, but this is the only one they are responisble for. The right sum is the one they will use in most applications.
Lutemann 3 years ago