To determine the area under the function [tex]\( f(x) = 5 \)[/tex] over the interval from 3 to 9, we can follow these steps:
1. Identify the function and the interval:
- The function is [tex]\( f(x) = 5 \)[/tex], meaning it is a constant function and always equals 5 regardless of the value of [tex]\( x \)[/tex].
- The interval given is from [tex]\( x = 3 \)[/tex] to [tex]\( x = 9 \)[/tex].
2. Calculate the length of the interval:
- The interval length is the difference between the upper and lower bounds of the interval.
[tex]\[
\text{Interval length} = 9 - 3 = 6
\][/tex]
3. Determine the value of the function over the interval:
- Since [tex]\( f(x) = 5 \)[/tex] is a constant, its value is 5 over the entire interval.
4. Compute the area under the function:
- For a constant function over a specified interval, the area under the curve can be computed by multiplying the function value by the interval length.
[tex]\[
\text{Area} = f(x) \times \text{Interval length} = 5 \times 6 = 30
\][/tex]
Thus, the area under the function [tex]\( f(x) = 5 \)[/tex] over the interval from 3 to 9 is [tex]\( 30 \)[/tex] square units.
The correct answer is:
b. 30 square units
