Question

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

Answer 1

They equal because there both the same regions and they don't differ that's why

Answer 2

Before answering this question let us know what are net and total areas.

$\text{Net area}= \text{total area above x-axis}-\text{total area below x-axis}$

$\text{Total area}= |\text{total area above x-axis}|+|\text{total area below x-axis}|$

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 region is below x-axis. This is because we have to subtract area of region which is below x-axis from area above x-axis to get net area.