Final answer:
To find ∫4 f(x) dx from 0 to 4 for f(x) = 2, we calculate the area of a rectangle with width 4 and height 2, which gives us an area (and integral value) of 8.
Step-by-step explanation:
The question asks to calculate the definite integral of the function f(x) = 2 from x = 0 to x = 4. Since f(x) is a constant function, the area under the curve on the interval [0, 4] is simply the area of a rectangle with the width of the interval and the height equal to the value of the function, which is f(x) = 2. Thus, the area can be calculated as the product of the width, which is 4, and the height, which is 2.
To compute the definite integral, we use the formula for the area of a rectangle:
- Area = width × height
- Area = 4 × 2
- Area = 8
So, the answer to ∫4 f(x) dx from 0 to 4 is 8.