Average Value of a Piecewise Function
Consider the piecewise function defined by $$f(x)=\begin{cases} 2*x+1 & 0\le x<1 \\ 3*x-1 & 1\le x\le 2 \end{cases}$$. Which of the following expressions represents the correct calculation of the average value of $$f(x)$$ on the interval $$[0,2]$$?
A
$$\frac{1}{2}\int_{0}^{2} f(x)\,dx$$
B
$$\frac{1}{2}\left(\int_{0}^{1}(2*x+1)\,dx-\int_{1}^{2}(3*x-1)\,dx\right)$$
C
$$\int_{0}^{1}(2*x+1)\,dx+\int_{1}^{2}(3*x-1)\,dx$$
D
$$\frac{1}{2}\left(\int_{0}^{1}(2*x+1)\,dx+\int_{1}^{2}(3*x-1)\,dx\right)$$
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