Answer:
3m ≤ ∫ f(x) dx ≤ 3M, at limit of b, a
Step-by-step explanation:
Like the question asked, which property of integral was used.
Property 8 of integrals was the basis upon which the question was solved.
The property of the integral is used to solve the problem. The function is given below.
[tex]3m & \leq \int_a^b f(x)dx \leq 3M \end{aligned}[/tex]
The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
Suppose f has absolute minimum value m and absolute maximum value M.
We know that the property of the integral can be used.
If m ≤ f(x) ≤ M ∀ a ≤ x ≤ b. Then we have
[tex]m (b-a) \leq \int_a^b f(x) dx \leq M(b-a)\\[/tex]
Then we have
[tex]m \leq f(x) \leq M \ \ and \ \ 4 \leq x \leq 7[/tex]
This means that
[tex]\begin{aligned} m(7-4) & \leq \int_a^b f(x)dx \leq M(7-4)\\\\3m & \leq \int_a^b f(x)dx \leq 3M \end{aligned}[/tex]
More about the function link is given below.
https://brainly.com/question/5245372
