Determine the area (in units2) of the region between the two curves by integrating over the x-axis. y = x2 − 24 and y = 1

The area of the region between the two curves by integration over the x-axis is 9.9 square units.

Step-by-step explanation:

This case represents a definite integral, in which lower and upper limits are needed, which corresponds to the points where both intersect each other. That is:

Given that resulting expression is a second order polynomial of the form , there are two real and distinct solutions. Roots of the expression are:

and .

Now, it is also required to determine which part of the interval is equal to a number greater than zero (positive). That is:

and .

Therefore, exists two sub-intervals: and . Besides, in each sub-interval. The definite integral of the region between the two curves over the x-axis is:

The area of the region between the two curves by integration over the x-axis is 9.9 square units.

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