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Pani-rosa [81]
3 years ago
13

To three decimal places, find the average value of f(x) = 2x2 + 3 on the interval [0, 2].

Mathematics
1 answer:
salantis [7]3 years ago
7 0
The formula for the average value of a function is \frac{1}{b-a}  \int\limits^b_a {f(x)} \, dx where b is the upper bound and a is the lower.  For us, this formula will be filled in accordingly.  \frac{1}{2}  \int\limits^2_0 {(2x^2+3)} \, dx.  We will integrate that now: \frac{1}{2}[ \frac{2x^3}{3}+3x] from 0 to 2.  Filling in our upper and lower bounds we have \frac{1}{2}[( \frac{2(2^3)}{3}+3(2))-0] which simplifies to \frac{1}{2}( \frac{16}{3}+6) and \frac{1}{2}( \frac{16}{3}+ \frac{18}{3})= \frac{1}{2}( \frac{34}{3}) which is 17/3 or 5.667
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