This article will illustrate how to **calculate area under a curve using integration** in Excel with instructional images and detailed discussion.

**Table of Contents**hide

## Download Practice Workbook

You can download the following practice workbook for your exercise or any kind of use.

## Necessary Formulas to Find the First Integral of Polynomial Trendline Equation in Excel

To find **area under curve** in Excel, we use the **trendline equation** generated by Excel. Polynomial trendline type is the best in this case.

The following is a **generic equation of a polynomial line**.

The **generic equation for the first integral** is-

For a **2nd degree polynomial**, the formulas will be-

and,

Where **I**** _{1}** is a constant.

For a **3rd degree polynomial**, the formulas will be-

and,

Where **I**** _{2}** is a constant.

## Steps to Calculate Area Under Curve Using Integration in Excel

The following dataset shows some coordinates of a random curve.

Now you will learn how to find the area under the curve these coordinates create step-by-step.

### ðŸ“Œ Step 1: Set Data Properly and Create Scatter Chart

- Set your data in order and select any cell of your data. Then go to the
**Insert**tab and from the**Charts**group, select a suitable chart type. - Here we have selected the
**Scatter with Smooth Lines and Markers**option.

- As a result, a graph like the following will appear.

### ðŸ“Œ Step 2: Enable Trendline and Its Equation

- Now, click on the
**Chart Area**. - Then click the
**Chart Elements**button. - Then form the
**Trendline**dropdown, and select**More Options**.

The **Format Trendline** window will appear at the right.

- Click on the
**Polynomial**button. Then mark the**Display Equation on chart**checkbox.

The trendline equation will appear on the chart area. It is as follows:

**Y = 7.331X ^{2} + 19.835X + 82.238**

### ðŸ“Œ Step 3: Find the First Integral and Calculate Area Under Curve

- Create a table like the following and insert the following formula in
**cell F24**.

`=F23-F22`

- Now, copy the trendline equation and paste it into
**cell E19**. **Calculate the first integral with this equation**using the formulas we have discussed earlier in this article.- The
**generic formula for this 2nd-degree polynomial-first integral**will be as follows.

Hence, the first integral of Y is-

**Y _{1} = 7.331X^{3}/3 + 19.835X^{2}/2 + 82.238X+C**

- Now, input the following formula (or match it with your data) in
**cell F22**and copy it with the**fill handle**in**cell F23**.

`=7.331*E22^3/3+19.385*E22^2/2+82.238*E22`

- As we see, the area is there in
**cell E24**.

**ðŸ’¬**** Note:**

This area under the curve is with respect to the X axis. If you want to find the area under the curve with respect to the Y axis then just flip the data horizontally, switch the axes, and apply all those steps described already.

**Read More:** **How to Make First Derivative Graph on Excel (With Easy Steps)**

## How to Calculate Area Under Curve in Excel Using Trapezoidal Rule

**Doing integration** is not an easy task for those who do not have basic knowledge of calculus. Here we come up with an easier way to find the area under any curve, the **Trapezoidal Rule**.

**ðŸ“Œ**** Steps:**

- First off, put the following formula in
**cell D5**and hit the**Enter**button.

`=((C6+C5)/2)*(B6-B5)`

- Now drag the
**fill handle**icon to**cell D14**. Leave the last as it is. - Insert the following formula in
**cell D16**.

`=SUM(D5:D15)`

- Press the
**Enter**key.

- You will see the output!

**ðŸ’¬**** Note:**

More coordinates in the same range with smaller intervals will give a more accurate result.

**Read More:** **How to Do Trapezoidal Integration in Excel (3 Suitable Methods)**

## Conclusion

So we have discussed how to calculate the area under a curve in Excel using integration. Moreover, we also have shown the use of the trapezoidal rule. Please leave us your feedback in the comment box.

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