# Finding area bounded Supposedly easy yet I have no clue

## Homework Statement

Use the left endpoint graph with the given number of
rectangles to approximate the area bounded by the
curve f (x), the x-axis, and the line x = 4.
f(x)=x2+x

No idea.

## The Attempt at a Solution

Once again, not a clue how to start this.

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• graph.bmp
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## Homework Statement

Use the left endpoint graph with the given number of
rectangles to approximate the area bounded by the
curve f (x), the x-axis, and the line x = 4.
f(x)=x2+x

No idea.

## The Attempt at a Solution

Once again, not a clue how to start this.

Well, you are calculating the area of each rectangle, and then adding the areas up. You are using 4 rectangles from (0,4). So, you know the length of each rectangle. How do you find the height? Look at where the rectangles touch the graph (i.e., the left endpoint of the rectangle).

Okay, I kind of guessed my way through it based on my notes and came up with 88/3 or 29.3333_ . Now, the next question asks me to do the same thing, but use the right endpoint graph. Wouldn't the answers be the same?

Okay, I kind of guessed my way through it based on my notes and came up with 88/3 or 29.3333_ . Now, the next question asks me to do the same thing, but use the right endpoint graph. Wouldn't the answers be the same?

You are splitting up the interval (0,4) like this:

(0, 1) (1, 2) (2, 3) (3, 4).

Do you see which are the left and right endpoints?

Okay, I kind of guessed my way through it based on my notes and came up with 88/3 or 29.3333_ . Now, the next question asks me to do the same thing, but use the right endpoint graph. Wouldn't the answers be the same?
What did you do to calculate this? I came up with a different answer.

So for the left endpoints I just do A=b*h and then add them all up?

Same for the right?

So for the left endpoints I just do A=b*h and then add them all up?

Same for the right?
Yep, that's really all there is to a problem of this type. You want to split up the interval, calculate the height at whichever point you're using (left, right, mid), calculate the area of each rectangle, and sum them up.

This all leads in to how to calculate the REAL area under the curve, which basically has to do with splitting the interval into infinitely many rectangles!

Yeah that's what I'm doing now. That part's okay. Just a little long.