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Calculus/Integral of absolute value function

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Red wrote at 2010-03-24 03:22:41
Alon I agree with your strategy.  Just note that in your 2nd last line I think your initial 9/4 should be negative, in keeping with the -x^2 in the previous line.  This gives an overall result of 44.5 rather than 49. I have double-checked this in a computer.

- Red.  


Bobbadee wrote at 2011-03-24 17:22:14
Wait isn't the answer is actually 44.5, because the integral of abs 2x-3= 42.25 + 2.25= 44.5?

I checked on my calculator and it agrees...


Milly wrote at 2011-11-08 04:02:00
Correct method Alon but answer is actually 44.5 as it is -(1.5)^2 not (-1.5)^2.


John Gabriel wrote at 2012-12-21 05:05:38
=9/4 + 9/2 + 64 - 24 - 9/4 + 9/2

=49 .



Is incorrect.



=9/4 +  64 - 24 - 9/4 + 9/2

=44.5  



Is correct.



An easier way would have been to integrate the primitive function:  Let f'(x)=|2x-3|,    then   f(x) = [(2x-3)*|2x-3|]/4



So integrate f(x) from 0 to 8 to obtain 44.5.


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Alon Mandes

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Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

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