APFIVE Ranking Functions by Average Value
Consider the four functions listed in the table above over the interval $$[0,\pi]$$. Their average values are computed using the formula $$\frac{1}{\pi}\int_0^{\pi}f(x)\,dx$$. Rank these functions in increasing order of their average value. Express your answer as an ordering (separated by commas) of the functions, using the notation exactly as in the table (for instance, write $$\sin(x)$$ not “sine of x”).
| Function | Average Value over $$[0,\pi]$$ |
|---|---|
| $$\sin(x)$$ | $$\approx 0.6366$$ |
| $$x$$ | $$\approx 1.5708$$ |
| $$2$$ | $$2.0000$$ |
| $$x^2$$ | $$\approx 3.2899$$ |
A
$$x$$, $$\sin(x)$$, $$2$$, $$x^2$$
B
$$\sin(x)$$, $$x$$, $$2$$, $$x^2$$
C
$$\sin(x)$$, $$2$$, $$x$$, $$x^2$$
D
$$x^2$$, $$2$$, $$x$$, $$\sin(x)$$
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