Question

A calculator has accuracy up to 8 digits after the decimal place. The value of ∫₀^(2π) sin x dx when evaluated using this calculator by the trapezoidal method with 8 equal intervals, to 5 significant digits, is

Accepted Answer

The correct answer is (A) 0.00000. With h=2π/8=π/4, the 8 interior/end sine values pair up exactly by symmetry over a full period (sin at 0,π/4,π/2,...,2π sums with its opposite-sign partner to zero), so the trapezoidal estimate is exactly 0 analytically, and to 5 significant digits on an 8-digit calculator this evaluates as 0.00000.

Explanation