Average Value of a Function

Question

A student attempts to find the average value of the function $$f(x)=2x^2$$ on the interval $$[1,3]$$. Instead of calculating the value of the expression $$\frac{1}{3-1}\int_1^3 2x^2\,dx$$, the student evaluates the function at the midpoint of the interval, $$f\left(\frac{1+3}{2}\right)=f(2)$$. What is the error in the student's approach?

Accepted Answer

They mistakenly computed the average value by evaluating the function at the midpoint instead of computing the integral average over the interval.

Answer

They incorrectly applied the power rule during the integration process.

Answer

They calculated the median value instead of the average.

Answer

They misidentified the limits of integration, yielding an incorrect interval length.

Average Value of a Function

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