APFIVE During an experiment to analyze temperature variation over a day, a student sought to compute the average temperature modeled by $$f(x)=2*x^2$$ on the interval $$[1,3]$$. Instead of using the formula $$\frac{1}{3-1}\int_1^3 2*x^2\,dx$$, the student simply evaluated $$f\left(\frac{1+3}{2}\right)=f(2)$$ and reported this as the average temperature. What mistake did the student commit?
| Method | Result |
|---|---|
| Integration Average | (Computed Value) |
| Midpoint f((1+3)/2) | f(2) = 8 |
They incorrectly applied the power rule during the integration process.
They misidentified the limits of integration, yielding an incorrect interval length.
They mistakenly computed the average value by evaluating the function at the midpoint instead of computing the integral average over the interval.
They calculated the median value instead of the average.
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