Question

How do you find the area enclosed by the x-axis and the given curve `y=(6/x)` for x between -4 & -2?

Answer 1

Area `= int_-4^-2(6/x)dx = 6 ln (1/2)`

Explanation:

Simply integrate the function y=(6/x) between the bounds given, -4 and -2.

`int_-4^-2(6/x)dx = 6 int_-4^-2 1/x \ dx`

`" " =6 [ln |x|]_-4^-2`

`" " = 6 { ln |-2| - ln |-4 }`
`" " = 6 { ln 2 - ln 4 }`
`" " = 6 { ln (2/4) }`
`" " = 6 ln (1/2)`