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# Find some formulas for the integral of the step function [t]^2

1. For , prove

2. For , with , define

Draw the graph of on the interval .

3. Find all real such that

1. Proof. Let . Then is a partition of and is constant on the open subintervals of . Further, for . So,

The second to last line follows from this exercise (I.4.7, #6)

2. The graph is:

3. By inspection, we have, .