Let f ( x )= |x -2| and g ( x )= f ( f ( x )) | vedclass

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Question

$\int_{0}^{3} g ( x )- f ( x )=\int_{0}^{3}|| x -2|-2| d x -\int_{0}^{3}| x -2| d x$

$=\left(\frac{1}{2} 	imes 2 	imes 2+1+\frac{1}{2} 	imes 1 \

Vedclass · Accepted Answer

$1$

Vedclass · Answer

$\int_{0}^{3} g ( x )- f ( x )=\int_{0}^{3}|| x -2|-2| d x -\int_{0}^{3}| x -2| d x$

$=\left(\frac{1}{2} 	imes 2 	imes 2+1+\frac{1}{2} 	imes 1 	imes 1ight)-\left(\frac{1}{2} 	imes 2 	imes 2+\frac{1}{2} 	imes 1 	imes 1ight)$

$=\left(2+1+\frac{1}{2}ight)-\left(2+\frac{1}{2}ight)=1$

Let $f ( x )= |x -2|$ and $g ( x )= f ( f ( x )), x \in[0,4]$ Then $\int \limits_{0}^{3}(g(x)-f(x)) d x$ is equal to

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