When does the net area of a region equal the area of a region? When does a region's net area differ from a region's area?

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Solution

Area bounded by curve:
Let us know what are net and total areas.
Net area $=$ Total area above x-axis $-$ Total area below x-axis
Total area $=$ $|$ Total area above $x$ -axis $|$ $+$ $|$ Total area below $x$ -axis $|$
Now let us look at first part of our question. Net area of our region will be equal to total area of region when the whole region lies above $x$ -axis because then our whole region is positive.
The net area of a region will differ from the total area of the region when some part of our region is above $x$ -axis and some part of the region is below $x$ -axis. This is because we have to subtract the area of the region which is below the $x$ -axis from the area above the $x$ -axis to get the net area.

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When does the net area of a region equal the area of a​ region? When does a region's net area differ from a region's area?

When does the net area of a region equal the area of a region? When does a region's net area differ from a region's area?