Question

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

Answer 1

so what are the subintervals?
1-1.5, 1.5-2, 2-2.5, 2.5-3
midpoints?

Answer 2

I'm gonna be honest this problem is greek to me....

Answer 3

well, it's a way of estimating the area under the curve. do you see that? know what it's about?

Answer 4

actually, here the average value of the function
we divide the interval into pieces, pick some points, compute f(x) at each point, and divide by the number of points.

Answer 5

Ok so that makes sense.....

Answer 6

So random points in each interval?

Answer 7

No, read the problem again.

Answer 8

mid points

Answer 9

of subintervals?
1-1.5, 1.5-2, 2-2.5, 2.5-3

Answer 10

How do I find those

Answer 11

midpoint of 1-1.5 = 1.25
midpoint of 1.5 -2 = ?

Answer 12

oh I get it so now I just substitute those values for x?

Answer 13

1.5-2=1.75

Answer 14

we divide the interval into pieces, pick some points, compute f(x) at each point, and divide by the number of points.

Answer 15

the points being 1.25, 1.75, 2.25, 2.75

Answer 16

so something like 3(1.25)^5+3(1.75)^5+...

Answer 17

I'm not very good at arithmetic :)

Answer 18

ok but is my thought process correct? then I just divide by the number of subintervals (4)

Answer 19

so it would be 3(1.25)^5+3(1.75)^5+3(2.25)^5+3(2.75)^5=703.22
703.22/4=175.8

Answer 20

Yes