# Estimating area under the graph

• hahaha158
In summary, the conversation discusses the task of estimating the area under the graph of a specific function using six approximating rectangles and right endpoints. The individual asking for help has tried multiple times but is unsure if they are on the right track, and presents a formula that is later determined to be incorrect. It is suggested to draw the rectangles to better understand the problem.
hahaha158

## Homework Statement

Estimate the area under the graph of f(x)=3+x^2 from x=−1 to x=2 using six approximating rectangles and right endpoints.

## The Attempt at a Solution

I've tried this multiple times but can't seem to get it, can someone tell me if i am on the right track?

i have

summation [3/6(3+(-1+i/6)^2)]

where i starts at -1 and increases by .5 passing through (-1,-0.5,0,0.5,1,1.5)

(I'm not sure about how the i increases)

Can anyone tell me what i am doing wrong?

Show the widths and heights of your 6 rectangles.

hahaha158 said:

## Homework Statement

Estimate the area under the graph of f(x)=3+x^2 from x=−1 to x=2 using six approximating rectangles and right endpoints.

## The Attempt at a Solution

I've tried this multiple times but can't seem to get it, can someone tell me if i am on the right track?

i have

summation [3/6(3+(-1+i/6)^2)]

where i starts at -1 and increases by .5 passing through (-1,-0.5,0,0.5,1,1.5)
This is an error. Because you are using right endpoints, the heights of the rectangles are determined at -0.5, 0, 0.5, 1, 1.5, and 2.

(I'm not sure about how the i increases)

Can anyone tell me what i am doing wrong?
I would second SteamKing's suggestion that you actually draw the rectangles. You seem to be trying to apply a formula without understanding it.

## 1. What is the purpose of estimating the area under a graph?

Estimating the area under a graph can help determine the total amount or quantity of something, such as the total volume of a liquid, based on a visual representation of its changing values over time or distance. This can be useful in many scientific fields, including physics, chemistry, and biology.

## 2. How is the area under a graph estimated?

The area under a graph is typically estimated by breaking it down into smaller, simpler shapes such as rectangles, triangles, or trapezoids. The areas of these shapes are then calculated and added together to provide an estimate of the total area under the graph.

## 3. What are some common methods used to estimate the area under a graph?

The most commonly used methods for estimating the area under a graph include the trapezoidal rule, Simpson's rule, and the midpoint rule. These methods vary in complexity and accuracy, and the most appropriate method to use will depend on the shape and complexity of the graph.

## 4. Can the area under a graph be negative?

No, the area under a graph cannot be negative. The area represents a quantity, and a negative area would indicate a negative quantity, which does not make sense in most scientific applications. If the graph represents a situation where negative values are possible, the area above the x-axis can be considered positive, while the area below the x-axis is considered negative.

## 5. What are some potential sources of error when estimating the area under a graph?

There are several potential sources of error when estimating the area under a graph. These include using an inappropriate method for the type of graph, not using enough subintervals to accurately approximate the shape, and measurement errors in determining the values on the graph. Additionally, human error in calculating and adding the areas of the smaller shapes can also contribute to inaccuracies in the final estimate.

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