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Given F=ax+b if x<1 F=(ln x)^2+1, x>1, calculate integral from 1 to e 1/(x*F)?
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On the interval (1,e] the function is defined as:
Using integration by substitution:
`u=lnx` and `du = dx/x`
The derivative of `tan^-1(x)=1/(1+x^2)` ; therefore:
Substituting `u=lnx` :
For the closed end of the interval, x=e:
For the open end of the interval` x-gt1^-` we must take the limit as x approaches 1 from the left. We can simply substitute x=1 into the function because the function is defined and continuous at x=1.
Posted by crmhaske on May 26, 2013 at 7:03 PM (Answer #1)
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