Calculate the value of the integral 1/x^2 going from 1 to b where b is a finite number greater than 1. Does the value of the integral approach a limit as b tends to infinity? (it does) If so, what is the value?
Calculate the value of the integral 1/x^2 going from 1 to b where b is a finite number greater than 1. Does the value of the integral approach a limit as b tends to infinity? (it does) If so, what is the value?
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$\displaystyle \int_1^b x^{-2} dx$
$\displaystyle -x^{-1}|_1^b$
$\displaystyle 1^{-1}-b^{-1}$
$\displaystyle 1-\frac{1}{b}$
Now, take the limit of this as b approaches infinity...