First Principles.. (1 Viewer)

[XcarvengerX]

It is interesting to see Lazarus posting three posts within 80 minutes. I think edit button has not been implemented then...

 

[acmilan]

Chances are the people who posted in between his were deleted

 

[PC]

I like it.

 

[fishy89sg]

sorry, i forgot i went to the last page of mathematics posts and read this thread and got distracted by another thread so i forgot that this was a 2002 thread :burn:

hmm seems ive completely forgotten about this thanks for the bump fishy

np

 

[mica]

Yes, both differentiation and integration from first principles are examinable.

Differentiation (example):
..lim.......f(x+h) - f(x)
h -> 0............h

Integration (example):
Integral[sqrt(r^2 - x^2)] between -r and r
Use A = (Pi*r^2)/2.

what ?

I have no idea what first principles intergration is, so could someone intergrate

f'(x) = 3x^2 using first principles intergration ? Please .


Surely theres no such thing !!!

 

[airie]

^Isn't that where you divide the area under the curve into infinitely many strips and take the limit of both its upper bound and lower bound? Surely it should be somewhere in a year 11 textbook...

 

[SoulSearcher]

Well there is, but it's rarely examined. Quoted verbatim from the Cambridge Year 11 3 Unit textbook:

To find a definite integral by first principles, dissect the interval into n equal subintervals, construct upper and lower rectangles on each subinterval, and find the sums of the upper and lower rectanlges. Then their common limit till be the value of the integral.

This is only for definite integrals, and thus to do your question, you would have to split the interval into n such intervals and then find limits of the upper and lower rectangles.

Or something like that, I don't know how to do these sorts of things