Lower and upper estimates for area under a curve using rectangles

[afcwestwarrior]

Homework Statement

by reading values from the given graph of f, use five rectangles to find a lower estimate and an upper estimate for the area under the given graph of from x=0 to x=10. in each case sketch the rectangles that you use.

The Attempt at a Solution

since their are there are 5 rectangles, the width was 2 for each of them

and when i tried to figure out the lower and upper estimate i did this

L5= 2*O^2+ 2*2^2 ... 2 * 8^2 =128

and the answer in the back of the book is 40

and for Right end= 2*2^2 ... 2*10^2= 440

and the answer is 52

 

[afcwestwarrior]

i already did sketched the rectangle thing, and it doesn't tell me what type of graph it is, it just tells me y= f(x)

 

[Dick]

The area of a rectangle is length*width. There is no 'square' in the formula.

 

[afcwestwarrior]

ok, so then i don't have to square them,

 

[afcwestwarrior]

i was looking at an example that was squaring them, no wonder, thanks man, i didn't think about the y= f(X)

 

[afcwestwarrior]

ok so what do i do then

 

[afcwestwarrior]

i didnt square the left end points and i got 40
but i did the same for the right end and i got 60

 

[Dick]

You must be able to determine the values of f(0), f(2) etc from your graph. Those are the heights. The widths are all 2.

 

[afcwestwarrior]

how do i do that, what formula do i use

 

[Dick]

If you are going to get a numerical answer like 52 then you must be able to find f(0) etc. It's the y value of the graph when x=0 etc.

 

[afcwestwarrior]

i did it, i multiplied 2 * the hieght, for every one

 

[Dick]

And got 52 for one of them?

 

[afcwestwarrior]

yup, i got 53, but then i took a closer look at the heights and got 52

 

[afcwestwarrior]

thanks for the help