Question

Consider Integral of (x^2+x)dx from 1 to 3 using Riemann sums. If u divide the interva from 1 to 3 into N subintervals, what will bethe length of each subinterval? What will be those subintervals?

Answer 1

The length of each subinterval will be (total length)/(number of subintervals)
Total length = top limit - bottom limit = 3 - 1 = 2
number of subintervals = N
length of each subinterval = 2/N

The first subinterval goes from 1 to 1 + 2/N
The 2nd from 1 + 2/N to 1 + 4/N
The 3rd from 1 + 4/N to 1 + 6/N

The kth from 1 + 2(k-1)/N to 1 + 2k/N

The nth (last) from 1 + 2(N -1)/N to 1 + 2N/N which is 3.