Use a finite sum to estimate the average value of the function on the given interval by partitioning the interval and evaluating the function at the midpoints of the subintervals.

f(x) = 3x^5 on [1, 3] divided into 4 subintervals

Question

Use a finite sum to estimate the average value of the function on the given interval by partitioning the interval and evaluating the function at the midpoints of the subintervals.

f(x) = 3x^5 on [1, 3] divided into 4 subintervals

anonymous · Answer

your interval has length 2, so if you divide it in to four parts they will have length $\frac{1}{2}$

anonymous · Answer

the intervals will have endpoints at 
$$1,1.5,2,2.5,3$$ and if you go half way between each the midpoints will be at 
$$1.25,1.75,1.25,2.75$$

anonymous · Answer

your job is therefore to evaluate the function at each of these points, add up the total, and then divide the result by the length of the interval, which is 2

anonymous · Answer

how do i evaluate it

anonymous · Answer

$$f(x) = 3x^5 $$
$$f(1.25)=4(1.25)^5$$ etc
use a calculator

anonymous · Answer

added them up and divided by 2. i assumed that 4(1.25)^5 was a typo. i used 3(x)^5. so after dividing by 2 i got 270.299804688