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# Calculus/Integral of absolute value function

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.

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.

Calculus

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