What is #f(x) = int 1/x # if #f(2)=1 #?

1 Answer
Jim G.
May 3, 2016

#ln(x/2)+1#

Explanation:

The derivative of #lnx=1/x #

hence the anti-derivative of #1/x" is"lnx#

#rArrF(x)= int1/x dx=lnx+c#

To find c , use f(2) = 1

ln2 + c = 1 → c = 1 - ln2

#rArr F(x)=lnx+1-ln2#

using #• lnx-lny=ln(x/y)"to simplify"#

#rArr int1/x dx= ln(x/2)+1#

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