From Förberedande kurs i matematik 2

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-	{{NAVCONTENT_START}}	+	The modulus function, <math>|x|</math>, strips <math>x</math> of its sign, e.g.
-	<center> [[Image:2_1_1d-1(2).gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+	{{Displayed math||<math>|-5|=5\,</math>, <math>\quad|3|=3\quad</math> and <math>\quad |-\pi|=\pi\,</math>.}}
-	{{NAVCONTENT_START}}	+
-	<center> [[Image:2_1_1d-2(2).gif]] </center>	+	For positive values of <math>x</math>, the modulus function has no effect, since
-	{{NAVCONTENT_STOP}}	+	<math>|x|=x</math>, but for negative <math>x</math> the modulus function changes the sign of <math>x</math>, i.e. <math>|x|=-x</math> (remember that <math>x</math>
		+	is negative and therefore <math>-x</math> is positive).
		+
		+	If we draw a graph of <math>y=|x|</math> it will consist of two parts. For
		+	<math>x\ge 0</math> we have <math>y=x</math>, and for <math>x\le 0</math> we have
		+	<math>y=-x\,</math>.
		+
		+	[[Image:2_1_1_d1.gif|center]]
		+
		+	The value of the integral is the area of the region under the graph <math>y=|x|</math> and between <math>x=-1</math> and <math>x=2</math>.
		+
		+	[[Image:2_1_1_d2.gif|center]]
		+
		+	This region consists of two triangles and we therefore obtain
		+
		+	{{Displayed math||<math>\int\limits_{-1}^{2} |x|\,dx = \frac{1}{2}\cdot 1\cdot 1 + \frac{1}{2}\cdot 2\cdot 2 = \frac{5}{2}\,\textrm{.}</math>}}

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Current revision

The modulus function, \displaystyle |x|, strips \displaystyle x of its sign, e.g.

\displaystyle |-5|=5\,, \displaystyle \quad|3|=3\quad and \displaystyle \quad |-\pi|=\pi\,.

For positive values of \displaystyle x, the modulus function has no effect, since \displaystyle |x|=x, but for negative \displaystyle x the modulus function changes the sign of \displaystyle x, i.e. \displaystyle |x|=-x (remember that \displaystyle x is negative and therefore \displaystyle -x is positive).

If we draw a graph of \displaystyle y=|x| it will consist of two parts. For \displaystyle x\ge 0 we have \displaystyle y=x, and for \displaystyle x\le 0 we have \displaystyle y=-x\,.

The value of the integral is the area of the region under the graph \displaystyle y=|x| and between \displaystyle x=-1 and \displaystyle x=2.

This region consists of two triangles and we therefore obtain

\displaystyle \int\limits_{-1}^{2} |x|\,dx = \frac{1}{2}\cdot 1\cdot 1 + \frac{1}{2}\cdot 2\cdot 2 = \frac{5}{2}\,\textrm{.}