Final answer:
The upper and lower bounds for ∫[-1,3] f(x)dx, where -2 ≤ f(x) ≤ 5, are 20 and -8 respectively.
Step-by-step explanation:
If we have the function f(x) such that -2 ≤ f(x) ≤ 5 on the interval [-1,3], we are looking for the upper and lower bounds of the definite integral of f(x) from x = -1 to x = 3. To find the bounds for the integral, we can multiply the length of the interval by the maximum and minimum values of f(x) over that interval, respectively. Since the minimum value of f(x) is -2 and the maximum is 5, the integral bounds are calculated as:
- Lower Bound: (-2) × (3 - (-1)) = -8
- Upper Bound: 5 × (3 - (-1)) = 20
The upper and lower bounds for ∫[-1,3] f(x)dx are 20 and -8, respectively.