What is the integral of #|x|#?

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What is the integral of #|x|#?

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Answer 1 · 2014-12-17T21:49:54

Let's take #a<0# and #b>0#, then #int_a^b |x|dx = int_a^0-xdx + int_0^bxdx = int_0^-axdx + int_0^bxdx = [1/2x^2]_0^-a +[1/2x^2]_0^b= 1/2(-a)^2+1/2b^2 = 1/2a^2+1/2b^2#

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What is the integral of #|x|#?

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