What is the difference between signed area and total area?
A plain definite integral gives signed area (below-axis parts subtract); total (geometric) area needs you to split at the roots and add the absolute values.
A plain definite integral gives signed area (below-axis parts subtract); total (geometric) area needs you to split at the roots and add the absolute values. A reliable way to keep them apart is to focus on what each one is defined by, not just the similar-sounding words.
Key point
signed area vs total area
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