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# How to Calculate Area Under Curve in Excel?

Are you trying to calculate the area under a curve in Excel but don’t know how? This article will show you how easy it is to do this task with a few simple steps. Whether you are a student, business professional, or simply someone who needs to calculate the area under a curve, this guide will walk you through each step of the process. With this comprehensive guide, you will have no problem calculating area under a curve in Excel. Let’s get started! ## Understanding the Concept of Area Under a Curve

In mathematics, the area under a curve is a measure of the space occupied by the curve. It is usually expressed in square units and is a fundamental concept used in calculus and other branches of mathematics. Area under a curve is usually calculated using the integral calculus. In the case of a rectangular or a triangular graph, the area can be calculated by simply multiplying the base and the height. In Excel, the area under a curve can be calculated using the built-in formula named AREA.

### Understanding the AREA Formula in Excel

The AREA formula in Excel is used to calculate the area under a curve in Excel. The formula takes two parameters as input – the upper and lower boundaries of the area to be calculated. The formula returns the area under the curve in square units.

The syntax of the formula is as follows:

AREA(lower_bound,upper_bound)

The lower_bound and upper_bound parameters specify the boundaries of the area to be calculated. The lower_bound must be lower than the upper_bound.

### Calculating Area Under a Curve in Excel

To calculate the area under a curve in Excel, we must first create a graph of the curve. This can be done by selecting the data points from a spreadsheet and plotting them on the graph. Once the graph is created, the area under the curve can be calculated using the AREA formula.

As an example, let us consider a graph of a function y = x2. To calculate the area under the curve, we must first determine the lower and upper boundaries of the graph. In our example, the lower boundary is 0 and the upper boundary is 4. Therefore, the AREA formula used to calculate the area under the curve is as follows:

=AREA(0,4)

The formula returns the value 32, which is the area under the curve.

## Using the AREA Formula to Calculate Area Under Multiple Curves

The AREA formula in Excel can be used to calculate the area under multiple curves. This can be done by using the SUM function to sum up the areas under each individual curve.

For example, let us consider a graph with two curves – y = x2 and y = x3. To calculate the area under both curves, we must first determine the lower and upper boundaries of both curves. In our example, the lower boundary for both curves is 0 and the upper boundary for both curves is 4. Therefore, the AREA formula used to calculate the area under the two curves is as follows:

=SUM(AREA(0,4), AREA(0,4))

The formula returns the value 64, which is the sum of the areas under both curves.

## Using the AREA Formula to Calculate Area Between Two Curves

The AREA formula in Excel can also be used to calculate the area between two curves. This can be done by subtracting the area under the lower curve from the area under the upper curve.

For example, let us consider a graph with two curves – y = x2 and y = x3. To calculate the area between the two curves, we must first determine the lower and upper boundaries of both curves. In our example, the lower boundary for both curves is 0 and the upper boundary for both curves is 4. Therefore, the AREA formula used to calculate the area between the two curves is as follows:

=AREA(0,4) – AREA(0,4)

The formula returns the value 32, which is the area between the two curves.

## Using the AREA Formula to Calculate Area Under a Curve with Multiple Boundaries

The AREA formula in Excel can also be used to calculate the area under a curve with multiple boundaries. This can be done by using the SUM function to sum up the areas of each individual boundary.

For example, let us consider a graph of a function y = x2 with three boundaries – 0, 2 and 4. To calculate the area under the curve, we must first determine the boundaries of the curve. In our example, the boundaries are 0, 2 and 4. Therefore, the AREA formula used to calculate the area under the curve is as follows:

=SUM(AREA(0,2), AREA(2,4))

The formula returns the value 24, which is the sum of the areas under each boundary.

## Top 6 Frequently Asked Questions

### 1. What is the formula for calculating area under curve in Excel?

The formula for calculating area under curve in Excel is SUMPRODUCT(A2:A5,TREND(B2:B5,A2:A5)). This formula takes the data points from column A and B, and uses the TREND function to determine the equation of the curve, then uses the equation to calculate the area under the curve. The SUMPRODUCT function is used to sum up the values of the area under the curve.

### 2. How do you create a graph in Excel to visualize the area under the curve?

To create a graph in Excel to visualize the area under the curve, first select the range of data points that you want to graph. Go to the Insert tab and select the chart type you want to use. Then right click on the chart and select “Add Trendline”. Select “Polynomial” as the type of trendline and adjust the order to fit your data. This will create a graph that shows the area under the curve.

### 3. What types of data can be used to calculate area under curve in Excel?

The data used to calculate area under curve in Excel can be any type of numerical data. This includes data points from linear, polynomial, exponential and logarithmic functions, as well as data points from any other type of mathematical function.

### 4. How do you determine the equation of the curve in Excel?

The equation of the curve can be determined in Excel using the TREND function. This function takes the data points from column A and B, and creates an equation that best fits the data. This equation can then be used to calculate the area under the curve.

### 5. How do you calculate the area under the curve in Excel?

The area under the curve can be calculated in Excel using the SUMPRODUCT function. This function takes the data points from column A and B, and uses the equation of the curve created by the TREND function to calculate the area. The result of the SUMPRODUCT function is the area under the curve.

### 6. What are the advantages of using Excel to calculate area under curve?

The main advantage of using Excel to calculate area under curve is that it is easy to use and it is more accurate than manual calculations. Excel also offers a wide range of functions that can be used to analyze data, such as graphical displays and statistical functions. Additionally, Excel allows users to save and share their data, making it a great tool for collaborative work.

Calculating the area under a curve in Excel can be a time-consuming task, but it is definitely worth the effort. With a few simple steps, you can quickly and easily find the exact area underneath any curve. Whether you are a student, teacher, or professional, understanding how to calculate the area under a curve in Excel is an invaluable skill that can help you save time and make more accurate calculations. With this knowledge, you can confidently tackle complex calculations with ease.