# How to Use Integration in Excel to Find Area Under a Curve

The following dataset shows some coordinates of a random curve.

### Step 1 – Set Data Properly and Create Scatter Chart

• Set your data in order and select any cell of your data. Go to the Insert tab and from the Charts group, select a suitable chart type.
• We have selected the Scatter with Smooth Lines and MarkersÂ option.

• The scatter chart will be inserted.

### Step 2 – Enable Trendline and Its Equation

• Click on the Chart Area.
• Click the Chart ElementsÂ button.
• From the Trendline dropdown, select More Options.

The Format Trendline window will appear.

• Click on the PolynomialÂ  and check the Display Equation on chart checkbox.

The following trendline equation will appear on the chart area.

Y = 7.331X2 + 19.835X + 82.238

### Step 3 – Find the First Integral and Calculate Area Under Curve

• Create a table and insert the following formula in cell F24.
`=F23-F22`

• Copy the trendline equation and paste it into cell E19.
• Calculate the first integral with this equation using the following formula.

The first integral of Y is-

Y1 = 7.331X3/3 + 19.835X2/2 + 82.238X+C

• Enter 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`
• The area is calculated in cell E24.

Note:

The 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, flip the data horizontally, switch the axes and apply all the steps described.

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

Steps:

• Insert the following formula in cell D5 and press Enter.
`=((C6+C5)/2)*(B6-B5)`
• 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 Enter.

• It will output the value of area under curve.

Note:

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

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