Final answer:
To find the area between y=x+2 and y=x² -2, we solve for the points of intersection, set them as the limits of integration, and then calculate the definite integral of the difference between the two functions.
Step-by-step explanation:
To find the area between the curves y=x+2 and y=x² -2, we first need to determine the points of intersection. This involves setting the two equations equal to each other and solving for x:
x + 2 = x² - 2
x² - x - 4 = 0
This quadratic equation can be solved to find the limits of integration, x1 and x2. After calculating the points of intersection, we integrate the difference between the two functions from x1 to x2 to find the area:
∫ (x + 2) - (x² -2) dx = ∫ (4 - x²) dx
The result will give the area between the curves, rounded to two decimal places as requested.
Remember to integrate with respect to x and to apply the limits of integration properly.