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How to plot a region correctly

In JEE Mains and Advanced problems, especially when it comes to calculating areas bounded by curves, one of the initial challenges students often face is correctly plotting the region in question. This can be particularly true for complex shapes or when dealing with inequalities that define regions not immediately intuitive to visualize. If you find yourself grappling with how to plot these regions effectively, you're not alone. The following discussion aims to shed light on a systematic approach that can simplify this process, making it not just manageable but also insightful.