Final answer:
The integral of a continuous constant function f(x) from 5 to 20 would yield 3.75, which is not present in the given options. There appears to be an error in the question or answer choices.
Step-by-step explanation:
The question involves applying the properties of continuous functions and definite integrals. Given ∫1^5 f(4x) dx = 5, we need to determine the value of ∫5^20 f(x) dx. First, we notice that f(x) is likely a constant function, since the area under the function f(x) from 1 to 5, scaled by 4 (due to the 4x inside the integral), yields a constant area of 5. Considering f(x) to be a horizontal line, as mentioned in the reference information, we can write f(x) = c, with c being a constant. The integral of a constant from 1 to 5 multiplied by 4 (due to the change of variable) is 4c*(5-1) = 20c, which is given as 5. Therefore, c = 5/20 = 1/4. Now, we can easily calculate the required integral by integrating f(x) = 1/4 from 5 to 20, which gives us (1/4)*(20-5) = 15/4 = 3.75.
Since none of the answer choices (20, 25, 30, 35) match 3.75, and since we are expecting an integer answer due to the discrete answer choices, it seems there may be an error in the initial statement or in the provided answer choices. However, with the information given and assuming the function f(x) is constant as suggested, the integral from 5 to 20 would not yield any of the provided answer options.