Trapezoidal rule

Calculus Level 5

Consider the integral I=0πsin2(x)dx. I = \int_0^\pi \sin^2(x) \, dx. Let EN=ITN E_N = I - T_N be the error in estimating I I using the trapezoidal rule with N N equal-sized intervals. (TN T_N is the estimate.)

What is 100E100, 100E_{100}, to three decimal places?

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