Mathematics

Problem

On the interval

[0,1]

two functions are given:

r(x)=e^{2x}

and

s(x)=2x+3

. (a) Compute the average value of

r

[0,1]

. (b) Compute the average value of

s

[0,1]

. (c) Determine by how much the average value of

r

exceeds (or falls short of) the average value of

s

Intuitive explanation

The average value of a function on an interval is found by integrating it and dividing by the interval's length—it's the height of a rectangle with the same area under the curve. Here you'll compute this for an exponential and a linear function, then compare them to see which grows faster on average over $[0,1]$ .

Intuitive explanation

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