37) The Area Under a Curve: approx. the definite intergral

[elephono73]

@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

[Lutemann]

I used the fundamental theorem of calculus.

[denissjacenko]

how did you get 26/3?

[Guilletube331]

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.

[frostwow]

5 stars yea.. sorry no stars in the rating system anymore

anyway thanks a lot

[pgdrums12]

at the end you said twenty three thirds instead of twenty 26 lol.

Great video though, 5 stars

[mrhnm]

why did the roots of the squares increase? i.e x1= 1.5, x2=2, x3=2.5etc...?

[siftthroughthestatic]

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

[mrhnm]

Thanks

[Roelandvinken]

why did you use n=4?? or is it just an arbitrairy choice

thanx for sharing the knowledge

[Lutemann]

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.

[dannysaurusrex]

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.

[Lutemann]

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.

[CorbeauBlanc]

thanks! :)

[milesgti]

extremely helpful

[HighLarious]

Very helpful -- thanks a lot!

[tmcsrr]

its not bad