Final answer:
To find the area between the graphs of f(x) = 4 – x² and g(x) = 4x + 7 for x in the interval –2 ≤ x ≤ 0, determine the points of intersection and then integrate the difference between the two functions over the interval.
Step-by-step explanation:
To find the area between the graphs of f(x) = 4 – x² and g(x) = 4x + 7 for x in the interval –2 ≤ x ≤ 0, you need to determine the points of intersection between the two graphs first. Set the two equations equal to each other: 4 - x² = 4x + 7. Rearrange the equation to get x² + 4x - 11 = 0 and solve for x using the quadratic formula or factoring. Once you have the points of intersection, you can integrate the difference between the two functions over the given interval to find the area.