anonymous
  • anonymous
Calculus - Determine the average value of f(x) over the interval form from x=a and x=b where f(x) = 1/x a= 1/7 and b= 7
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
\[\frac{ 1 }{(b-a)}\int\limits_{a}^{b} f(x) dx\]
anonymous
  • anonymous
I got -100/7
anonymous
  • anonymous
result is 4.0390

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anonymous
  • anonymous
\[\frac{ 7 }{ 48 } \int\limits_{1/7}^{7} \frac{ 1 }{ .5(7)^2}- \frac{ 1 }{ .5(1/7)^2 }\]
anonymous
  • anonymous
function is 1/x so it means to be solved in boundaries a and b
anonymous
  • anonymous
solutions of integral is 3.891
anonymous
  • anonymous
the rest is simple math
anonymous
  • anonymous
can you do the rest?
anonymous
  • anonymous
I got ln(7) - ln (1/7) which is 3.891...
anonymous
  • anonymous
then you multiply that by \[\frac{ 1 }{ b-a }\]
anonymous
  • anonymous
7-1/7= 6.857... which 1/8.857 * 3.891 is .5675...
anonymous
  • anonymous
yep
anonymous
  • anonymous
1/6.857 not 1/8.857
anonymous
  • anonymous
so as an exact answer it would be \[7\log 7/ 24\]
anonymous
  • anonymous
yep typo.

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