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Calculus/Integration of Absolute Values

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Expert: - 1/4/2011


Question
What is the definite integral of the absolute value of 2x-3 on the interval [0,3]?

Answer
The function is 0 at 2x - 3 = 0.  Add 3 to both sides and get 2x = 3, or x = 3/2.
Since 3/2 is in the middle of the interval [0,3], we have two functions.

On [0,3/2], the function is 3 - 2x, since 2x - 3 is negative in this interval.
On [3/2,2], the function is 2x - 3.

To do this, evaluate thie integral from 0 to 3/2 on the 1st function and
the integral from 3/2 to 2 on the 2nd function.

Note that when evaluating an integral of an absolute value,
the outcome should be positive.

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