Question

What is the net area between `f(x) = 2/(x+3)` and the x-axis over `x in [1, 2 ]`?

Answer 1

`ln(25/16)`

Explanation:

The area between the `x` axis and our function can be given by the integral of the function `f(x)` with the appropriate limits applied to the integral:

`int_1^2f(x)dx=int_1^2 2/(x+3)dx`

We can read the integral from a table of standard integrals to obtain:

`=[2ln|x+3|]_1^2`

Now applying the limits:

`={2ln|2+3|}-{2ln|1+3|}`

`=2(ln5-ln4)`

Applying our rules of logarithms to do a bit of tidying up and we get:

`=ln(25/16)`