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In the video tutorial, the definite integral of cosine two pi x DX from -2 to 2 is computed using two methods: a geometric approach and a formal algebraic approach. The geometric approach involves considering the periodicity of the cosine function, with a period of 1 due to the coefficient of x being 2 pi. By recognizing the function's sinusoidal nature and going through four periods on the integration interval, it is determined that the function spends half its time above zero. The algebraic approach is used to confirm this result, showing that both methods yield the same answer.
