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integral from 0 to pi/3 of 0.5 * (2sin(x))^2 + integral from pi/3 to pi/2 of 0.5 * (2sin(2x))^2
integral from 0 to pi/3 of 0.5 * (2sin(x))^2 + integral from pi/3 to pi/2 of 0.5 * (2sin(2x))^2
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