Trapezoidal rule

Calculus Level 5

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

What is \( 100E_{100},\) to three decimal places?

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