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

1. 0.00000
2. 1.0000
3. 0.00500
4. 0.00025

Correct answer: 0.00000

Solution

The integral of sin x over one complete period from 0 to 2π is zero, as the positive and negative areas cancel each other out. Therefore, when calculated using the trapezoidal method with high precision, the result remains effectively zero, which rounds to 0.00000.

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