# Integration : Area of a Bounded Region

Please help with the following problem. Provide step by step calculations for each.

The average value of f(x) = 1/x on the interval [4, 16] is

(ln 2)/3

(ln 2)/6

(ln 2)/12

3/2

0

1

none of these

Find the area, in square units, of the region bounded by the the x axis and the function y = 16 - x^2.

32/3

36

256/3

500/3

972

none of these

https://brainmass.com/math/integrals/integration-area-bounded-region-139465

#### Solution Preview

21. The average value of f(x) = 1/x on the interval [4, 16] is

(ln 2)/3

(ln 2)/6

(ln 2)/12

3/2

0

1

none of these

The answer is (ln 2)/6.

As by the definition, the average value of f(x) = 1/x on the interval [4, 16] is equal to the definite ...

#### Solution Summary

The area of a bounded region is found using integrals. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question. Step by step calculations are given.