Question

Find the area, for `y=1/x`, `y=x` and `y=x/4` (x>0) How would i find a and b intervals when given more than two functions?

Answer 1

See below

Explanation:

For area enclosed by these relations, you can write it like this:

`"Area" = int_0^1 x \ dx + int_1^2 1/x \ dx color(red)(- int_0^2 x/4 \ dx)`

`= ln(2)`

Diagram explains. You can do the first and last integration using triangles, and they cancel out.