4 attempts remaining. If $11 \leq f(x) \leq 20$, then \[ \leq \int_{1}^{7} f(x) d x \leq \] Submit answer Answers (in progress) Answer

Step 1 ：The question is asking for the possible range of the integral of the function f(x) from 1 to 7, given that the function is bounded between 11 and 20.

Step 2 ：The integral of a function over an interval can be thought of as the 'area under the curve' of the function on that interval. If the function is always at least 11 and at most 20 on the interval from 1 to 7, then the 'area under the curve' will be at least the area of a rectangle with height 11 and width 6 (the length of the interval from 1 to 7), and at most the area of a rectangle with height 20 and width 6.

Step 3 ：So, we need to calculate these two areas to find the possible range of the integral.

Step 4 ：Lower bound of the integral is \(11 \times 6 = 66\)

Step 5 ：Upper bound of the integral is \(20 \times 6 = 120\)

Step 6 ：Final Answer: The possible range of the integral of the function f(x) from 1 to 7 is \(\boxed{66 \leq \int_{1}^{7} f(x) d x \leq 120}\)