....have absolutely nothing to do with each other. And yet, when asked to sketch the domain of integration, consistently about 50% of the time calculus students will insist on trying to work the integrand into the sketch somehow, and then confuse themselves and make a mess of the integral. You should be making an effort to lose this impulse, because it will waste your precious time when you try to change the order of integration. Just look at the limits of integration and forget about the integrand until you've got the new order switched.
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