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Lösung 2.1:1d
Aus Online Mathematik Brückenkurs 2
The modulus function, x
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For positive values of x
=x
x
=−x
If we draw a graph of x
0
0
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{.} |