Question

Can someone plz help me with this question!!
Estimate the area under the curve f(x)= x^2 +2x for 0 less than or eqaul to x less than or equal to 1 by evaluating the riemanna sum with n=8, taking the sample points Ci to be the right-hand end points. Draw a pic illustrate the process

Answer 1

@IrishBoy123 @zepdrix

Answer 2

this is going to take a raft of arithmetic

Answer 3

divide the interval \((0,1)\) in to 8 parts, each will have length \(\frac{1}{8}=0.125\)

Answer 4

I have went through my book and notes trying to solve this but do not know how to do this.

Answer 5

the right hand endpoints will be\[.125,.25,.375,.5,.625,.75,.875,1\]

Answer 6

or if you perfer \[\frac{1}{8},\frac{2}{8},\frac{3}{8},\frac{4}{8},\frac{5}{8},\frac{6}{8},\frac{7}{8},\frac{8}{8}\]

Answer 7

you have to evalute the function at each right hand endpoint
add them up, and then multiply the result by \[\frac{1}{8}\]

Answer 8

use a speadsheet or sommat

Answer 9

it will not be fun, but it is totally doable \[\left(f(0.15)+f(.25)+f(3.75)+f(.5)\\
+f(6.25)+f(.75+f(.875)+f(1)\right)\times .125\]

Answer 10

damn typo, i am not writing it again

Answer 11

here's what the graph and rectangles look like (see the attached image)

Answer 12

that is impressive @jim_thompson5910

Answer 13

thanks, I had geogebra do all the work

Answer 14

will it compute the sum too?

Answer 15

t will not be fun, but it is totally doable
(f(0.125)+f(.25)+f(3.75)+f(.5)+f(6.25)+f(.75+f(.875)+f(1))×.125
okay what would f be? I understand the math par.

Answer 16

and @jim_thompson5910 thanks for the image I will def put that in my notes :)

Answer 17

\[f(x)=x^2+x\] so for example \[f(.125)=(.125)^2+.125\] lather rinse repeat

Answer 18

ok that was wrong \[f(x)=x^2+2x\] so
\[f(.125)=(.125)^2+2\times .125\]

Answer 19

yes, what you can do is draw up a spreadsheet like this

Answer 20

etc etc
did i mention it is a pile of arithmetic?
and not that useful either since the actual area very easy to find

Answer 21

looks good
take @jim_thompson5910 answer there and multiply it by \(.125\) the length of each interval

Answer 22

in cell C11, I typed in `Sum[C2:C10]`

and for some reason, I went too far, I should have just done `Sum[C2:C9]`, oh well

Answer 23

yeah u mentioned that it's a lot of arithmetic. But I need to fidn the area this problem is really confusing to me plz explain. and I like the way @jim_thompson5910 did okay I wwill do that @satellite73

Answer 24

it is the area of each rectangle

Answer 25

but still not sure how @jim_thompson5910 got those digits there.

Answer 26

each rectangle has height \(f(x_i)\) for the various \(x_i\) right hand endpoints, and each base is \(.125\) since you divided an interval of length one by eight

Answer 27

okay x is 1/8, 2/8, 3/8....