A sensor's reading during the time interval [0, 2] seconds is f(t) = 3t² + 1. What is the average value of f over this interval? Give the answer as an integer.

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Average sensor reading

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A sensor's reading during the time interval $[0, 2]$ seconds is $f (t) = 3 t^{2} + 1$ . What is the average value of $f$ over this interval? Give the answer as an integer.

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Hint

The average value is the integral divided by the length of the interval.

Solution

The integral of $3 t^{2} + 1$ from $0$ to $2$ is the change in $t^{3} + t$ between the limits.
That gives $8 + 2 - 0 = 10$ .
The interval has length $2$ , so the average is $\frac{10}{2} = 5$ .

Answer: $5$

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