Question 4 (1 point)What is the average value of on the interval [1, 5]? a4 b8 c2 d1 e16

Break Down the Problem

1. Identify the function to find the average value of.
2. Understand the formula for the average value of a function over an interval.
3. Calculate the average value using the identified function.

Relevant Concepts

The average value of a continuous function $f(x)$ on the interval $[a, b]$ is given by the formula:

$\text{Average Value} = \frac{1}{b - a} \int_{a}^{b} f(x) \, dx$

In this case, the function appears to be constant or simply represented as $f(x)$ over the interval $[1, 5]$.

Analysis and Detail

1. Let's assume $f(x) = x$ for interpretation.
2. Substitute $a = 1$ and $b = 5$ into the average value formula:

$\text{Average Value} = \frac{1}{5 - 1} \int_{1}^{5} x \, dx$

3. Compute the definite integral:

$\int x \, dx = \frac{x^2}{2} \Big|_{1}^{5} = \frac{5^2}{2} - \frac{1^2}{2} = \frac{25}{2} - \frac{1}{2} = \frac{24}{2} = 12$

4. Now calculate the average value:

$\text{Average Value} = \frac{1}{4} \times 12 = 3$

Verify and Summarize

The average value computed is 3. However, none of the provided options (a = 4, b = 8, c = 2, d = 1, e = 16) includes this result.

Final Answer

The computed average value over the interval [1, 5] is 3, which does not correspond to any of the options given. Please check the function again or the choices.