How do I solve this question in the most clear way? How to calculate the area of the region between the functions 12x-2, 2x^2 +6x-2 and the postive x-axis?

Answer 1

It appears the area is infinite.

Let y1 = 12x^2

Let y2 = 12x^2 + 6x - 2

For all positive x, y2 > y1

Also, y2 grows faster than y1 so as x increases, the difference between y1 & y2 becomes greater.

So, as x increases, the distance between the two functions increases.

Therefore, as x approaches infinity, the total area between the two functions also approaches infinity.