Question

I have a question regarding integrals and approximating areas. It gives me a graph, n=4, and my intervals(0,8) and asks me to find it through the midpoint method. where do i plug my numbers into after i have gone though the process of finding the midpoints?

Answer 1

you either have to go thru a reimann sum process or just use numerical methods like trap rule or simpsons

Answer 2

ya i need to go through the reimann sum, but i dont know how to do that

Answer 3

\[\sum_{k=1}^{4}f(c_k)\triangle x_k\]

Answer 4

\(\triangle x\) = \(\frac{b-a}{n}\)

Answer 5

f(Ck) ... that never looks good; is the value of f(x) at the midpoints

Answer 6

ya i have 2 as my delta x, and (1+3+ 5+ 7) as my numbers i need to plug in

Answer 7

yess

Answer 8

2(1) + 2(3) + 2(5) + 2(7)

2(1+3+5+7) then right?

Answer 9

yep thats how it lookss but the answer is 10

Answer 10

what is your function? hard to see if you made a mistake without it :)

Answer 11

i think you forgot to find the f(x) values for each midpoint and are just trying to use the midpoint itself as the value ...

Answer 12

the thing is that all it gives me is \[\int\limits_{0}^{8}\]f(x)dx and graph

Answer 13

can you determine what your values for f(x) are at each midpoint?

Answer 14

yes (1,3,5,7)

Answer 15

1,3,5,7 looks like the y=x function

f(1) = 1
f(3) = 3
f(5) = 5
f(7) = 7

which gives an area of 32 ... without being able to see your material; thats the best I can come up with

Answer 16

thank u, i appreciate it!

Answer 17

good luck with it; I gotta head to class :)