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Defining natural logarithm function in terms of the area under the curve.

Define the natural logarithm function in terms of the area under the curve in y=1/x in detail using the example below

We know that the area bounded by the curve f(t) = 1/t ,t taken in the interval[1,x]  is

G(x)= \ .

From figure 2, G(x) is an anti derivative of  f(x)=1/x

Please state at the end that ln(x) = Integral(1,x) 1/t dt


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