use a finite sum to estimate the average value of f on the given interval by partitioning the interval into four subintervals of equal length and evaluating the f at the subinterval midpoints.

f(x)=x^4 on [0,2]

Question

use a finite sum to estimate the average value of f on the given interval by partitioning the interval into four subintervals of equal length and evaluating the f at the subinterval midpoints.

f(x)=x^4 on [0,2]

anonymous · Answer

Midpoint formula I see, so let's  partition

0      .5           1         1.5             2

Since this is midpoint formula,we want to evaluate number in middle

 0.25     0.75       1.25     1.75

0.5((0.25)^2+(0.75)^2 +(1.25)^2 +(1.75)^2)

anonymous · Answer

This get evaluated to be 2.625

anonymous · Answer

Since this asked for average we multiply by 1/range = 1/2

anonymous · Answer

i received an answer of 2.63 but wasnt sure this was right.  so do i just divide that by 2??

anonymous · Answer

Yes, divide 2.63 by 2 to get aveage

anonymous · Answer

$$\text{Avarage}=\frac{1}{b-a}\int _a^bf(x)dx$$

anonymous · Answer

imranmeah91 do you mind taking a look at mine when u r done?

zarkon · Answer

3.03515625

zarkon · Answer

the average vlaue of a function given $$a<x_1<x_2<\cdots<x_n<b$$

is $$\frac{\displaystyle\sum_{i=1}^{n}f(x_i)}{n}$$