Reference no: EM131035801

In lectures, we estimated the area under the graph of y = x2 over the interval [0, b] by partitioning [0, b] into n equal subintervals, estimating the area under the curve over each of these subintervals, and adding up the resulting estimates. Then we were able to use a tricky formula to find the limiting value of these estimates as n became larger and larger.

Suppose that we try to do the same thing to find the length of the curve y = x2 over [0, b].

1. Given i ∈ {1,2,3,...,n}, write down the endpoints of the i-th interval Ii in a regular partition of [0, b] into n equal subintervals.
2. Let us approximate the curve y = x2 over Ii by a straight line joining the two ends of the curve (over this interval). Write down an expression for the length of this line, simplifying your expres- sion.
3. Now write down an expression involving the Σ symbol that will give the estimate for the length of the curve y = x2 over [0, b].