Calculate m6 for f(x)=4⋅ln(x^2) over [1,2].

In this we need to approximate definite integral by midpoint formula.
According to this formula if we have to calculate
then we will divide the interval [a,b] into n subinterval of equal width.
Δx =
So we will denote each of interval as follows
where
Then for each interval we will calculate midpoint.
So we can calculate definite integral as

where are midpoint of each interval.

So in given question we need to calculate . So we will divide our interval in 6 equal parts.
Given interval is [1,2]


So we will denote 6 interval as follows

Now midpoint of each interval is







So for the given function is


               
               
So