if we know that 12 is less than or equal to f(x) which is less than or equal to 18, what can be say about this inequality?
? is less than or equal to the definite integral from 3 to 10 of f(x) is less than or equal to ?
No clue how to approach this one? I know the integral is positive, that's all
a. f(x) is bounded between 12 and 18
b. I don't understand the question on this one.
I got it. its that the minimum area is found by saying that the function is a straight line at y=12 and the opposite for 18 and finding those areas under the integrals bounds
To determine the inequality involving the definite integral from 3 to 10 of f(x), we can start by considering the given information:
We know that 12 is less than or equal to f(x) and f(x) is less than or equal to 18 for all values of x.
Now, to find the inequality involving the definite integral, we need to consider the behavior of the function f(x) over the interval [3, 10] and how it affects the integral.
Here are the steps to approach this problem:
Step 1: Determine the behavior of f(x) over the interval [3, 10].
You can examine the given information to understand that f(x) lies between 12 and 18. This means that f(x) will always be positive over the interval [3, 10] because both lower and upper bounds are positive.
Step 2: Recall the relationship between a function and its definite integral.
If f(x) is a positive function over the interval [a, b], then the definite integral from a to b of f(x) will also be positive. This is because the integral represents the area under the curve, which in this case, is always positive.
Step 3: Apply the relationship to our problem.
Since f(x) is positive over the interval [3, 10], we can conclude that the definite integral from 3 to 10 of f(x) will be positive. Therefore, the inequality involving the definite integral is:
0 is less than or equal to the definite integral from 3 to 10 of f(x) is less than or equal to some positive value.
Note: The exact value of the definite integral cannot be determined without additional information about the function f(x). However, we can confidently say that the integral is positive based on the given conditions.
In summary, the inequality involving the definite integral from 3 to 10 of f(x) is: 0 is less than or equal to the definite integral from 3 to 10 of f(x) is less than or equal to a positive value.