Question

What is the net area between `f(x) = 4/x` and the x-axis over `x in [1, 2 ]`?

Answer 1

`4 ln2 ~~ 2.7725887...`

Explanation:

We seek the net area between `f(x) = 4/x` and the `x`-axis for `x in [1, 2 ]`.

We first note that `f(x)` has a disvontunitry at `x=0` and that this discontinuity is outside the desired range, and so is of no concern. Further noting that `f(x)` is continuous and positive over the desired range, the net area is given by:

`A = int_1^2 \ 4/x \ dx`
`\ \ = 4 [ \ ln |x| \ ]_1^2`

`\ \ = 4 (ln2-ln1)`

`\ \ = 4 ln2`