Numbers between 1 and 100 that are multiple of 3 but not multiple of 8
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Splitting up the interval [0, 6] into 6 subintervals means we have
![[0,1]\cup[1,2]\cup[2,3]\cup\cdots\cup[5,6]](https://tex.z-dn.net/?f=%5B0%2C1%5D%5Ccup%5B1%2C2%5D%5Ccup%5B2%2C3%5D%5Ccup%5Ccdots%5Ccup%5B5%2C6%5D)
and the respective midpoints are
. We can write these sequentially as 
where 
.
So the integral is approximately
Recall that
so our sum becomes
and the respective midpoints are
So the integral is approximately
Recall that
so our sum becomes