1. ## Unbounded Integral

Can someone help me with this integral?

Mathematically I got -3/2.

Intuitively(with some math) I got 1/2

My calculator got infinity

The integral is S((x-4)^(-2))dx from 3 to 6.

I don't feel like writing down my work as it may be wrong, but by looking at the equation from [3,5] the area should be zero and that leaves the interval [5,6] and the area under that portion of the curve is 1/2. But I need to show it in my work as (t -> 4 from the left) etc and then my calc says the integral diverges so can someone help me?

Thanks

2. Note that $\frac{1}{(x-4)^2}$ is not defined for $x=4$ and $4 \in [3,6]$.
So you are dealing with an improper integral.

3. Ugh, sorry I just mislabeled the title.