Chapter 1.2, Problem 124E

In the following exercises, compute the average value using the left Riemann sums L_N for N = 1, 10, 100. How does the accuracy compare with the given exact value?

124. Suppose that $A={\displaystyle {\int }_0^{2\pi }{\sin }^{2}tdt}$ and $B={\displaystyle {\int }_0^{2\pi }{\cos }^{2}tdt}$ . Show that

   $A+B=2\pi$ and A = B.