The area of the region bounded by the curve \(y = x\) and the x-axis, between the boundaries \(x = 0\) and \(x = 2\) is:
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When finding the area under simple linear graphs like \(y = x\) or \(y = mx + c\), verifying your integration result using basic geometric formulas for triangles or trapezoids is a quick way to catch arithmetic slips.