Is the positive and negative of double integral related to the positive and negative of integral closed region? For example, if the same integrand is positive, but the closed region is positive In the first quadrant and the fourth quadrant, does the double integral become negative? In addition, is the definite integral also related to the positive and negative of the closed interval? For example, if they are all the same positive integrands, will the closed interval affect the positive and negative of the definite integral on the positive and negative half axes?

No matter the integral interval is [- 1,0] or [0,1], the integral result is 1 / 3 > 0, that is to say, the positive and negative of the integral result is only determined by the positive and negative of the integrand, which has nothing to do with the integration area

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