1. ## Improper Integrals

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?

Thanks =)

2. Originally Posted by Merdiemae
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?

Thanks =)
$\int_1^b x^{-2} dx$

$-x^{-1}|_1^b$

$1^{-1}-b^{-1}$

$1-\frac{1}{b}$

Now, take the limit of this as b approaches infinity...

$lim_{b \rightarrow \infty} 1-\frac{1}{b} = 1$

3. Thank you so much!! I see what I did- stupid mistake- I had my answers backwards!! Ha ha =)