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

1 Answer
May 29, 2018

# 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 #