Average Value of a Piecewise Function

Question

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 $$[0,2]$$?

Accepted Answer

$$\frac{1}{2}\left(\int_{0}^{1}(2*x+1)\,dx+\int_{1}^{2}(3*x-1)\,dx\right)$$

Answer

$$\frac{1}{2}\int_{0}^{2} f(x)\,dx$$

Answer

$$\frac{1}{2}\left(\int_{0}^{1}(2*x+1)\,dx-\int_{1}^{2}(3*x-1)\,dx\right)$$

Answer

$$\int_{0}^{1}(2*x+1)\,dx+\int_{1}^{2}(3*x-1)\,dx$$

Rank	User	Correct Count	Attempt Count	Total Time	Score
#1	haneesh19.12	2	4	0m 00s	180
#2	sophieyao08	1	1	0m 59s	41
#3	bryantche0218	1	2	5m 09s	-219
#4	srinikasriyamathur	1	2	34m 19s	-1,969

Average Value of a Piecewise Function

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