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|dw:1353031457071:dw|

You basically want to find the area of the three rectangles. Make sense?

sort of? how would i find the area's ?

Well, for one, what is the area of a rectangle?

is it from 0 to 3?

I'm talking about in the general sense

Okay, I just wanted to say, the area of a rectangle is length times width.

So our first task is to find the width of the rectangles.

So what is the width of each rectangle?

ok

That is the width of the entire interval, not the width of each subinterval/rectangle

\[
\frac{3-0}{3} = 1
\]

oh ok. I see now b-a/n=1

Now, to find the length of the interval is a bit tricky.

We need to pick some x in each subinterval. The length is then f(x).

So the first interval is \(1*f(1) = 1 * 1^3 = 1\)

The second interval is between a+w and (a+w)+w

So the highest point is a+w+w = 0+1+1 = 2

So the second subinterval area is \(1*f(2) = 1*2^3=1*8=8\)

Do you think you can do the third sub interval?

can you tell me the steps sorry im not good at this?

|dw:1353032610122:dw|

are we adding the last f(3) to 8

the answer f(3) * 8

Nope. All I did was show that rectangle 1 has area 1, and rectangle 2 has area 8

1*3^3=27

27+8+1= 36

can you explain how the left hand works? to the same problem? it makes sense now? thank you!!!

|dw:1353033340267:dw|

ok

How do you understand how I'm getting them?

from the picture you drawn up you use the rectangles starting from the left to the right.