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  2. Calculus and Analysis
  3. Real Analysis
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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

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.

$2.19

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