**Method 1 – Calculate the Area Under the Curve with the Trapezoidal Rule in Excel**

It is not possible to directly calculate the area under the curve. We can break the whole curve into trapezoids. By adding the areas of the trapezoids, we can get the total area under the curve.

**STEPS:**

- Select the range
**B4:C11**from the dataset. - Go to the
**Insert**tab. - Select the
**Insert Scatter (X, Y)**option from the**Charts**section. - From the drop-down, select
**Scatter with Smooth Lines and Markers**option.

This will open a chart like the one below.

- Calculate the area of the trapezoid which is between
**X**=**1**&**X**=**3**under the curve by entering the following formula in cell**D5**:

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

- Press
**Enter**. - Use the
**Fill Handle**tool till the second last cell to get the area of the trapezoids.

- Add all the areas of the trapezoids by entering the following formula in cell
**D13**.

`=SUM(D5:D10)`

We have used **the SUM function** to add up the cell range **D5:D10**.

- Press
**Enter**to see the result.

**Method 2 – Use Excel Chart Trendline to Get Area Under Curve**

Excel Chart Trendline helps us to find an equation for the curve. We use this equation to get the area under the curve. Suppose, we have the same dataset containing different points on the **X **& **Y** axes in columns **B **& **C** respectively. We will use the chart trendline to get the equation from which we can get the area under the curve.

**STEPS:**

- Select the chart.

Select the range **B4:C11 **> go to **Insert **tab > select **Insert Scatter (X, Y) **from the drop-down > select **Scatter with Smooth Lines and Markers **option.

- Go to the
**Chart Design**tab. - Select
**Add Chart Element**drop-down from the**Chart Layouts**section. - From the drop-down, go to the
**Trendline**option. - Select
**More Trendline Options**.

- Or you can simply click on the
**Plus**(**+**) sign on the right side of the chart after selecting it. - This will open the
**Chart Elements**section. - From that section, place the cursor over the
**Trendline**section and click on**More Options**.

- In the
**Format Trendline**window, select**Polynomial**from the**Trendline Options**.

- Check the
**Display Equation on chart**option.

The polynomial equation will be displayed on the chart.

- The polynomial equation is:

**y = 0.0155×2 + 2.0126x – 0.4553**

- We need to get the definite integral of this polynomial equation which is:

**F(x) = (0.0155/3)x^3 + (2.0126/2)x^2 – 0.4553x+c**

**Note:**For getting a definite integral from an equation, we need to increase the power of the base (

**x**) by

**1**and divide it by the increased power value. In the above equation, the

**x**&

**x2**turns into

**x2/2**&

**x3/3**respectively. As well as, the constant

**0.4553**turns into

**0.4553x**.

- We will put the value
**x**=**1**in the definite integral. We can see the below calculation in cell**F8**:

`F(1) = (0.0155/3)*1^3 + (2.0126/2)*1^2 - 0.4553*1`

- Press
**Enter**to see the result.

- We will enter
**x**=**10**in the definite integral. The calculation will be like the following in cell**F9**:

`F(10) =(0.0155/3)*10^3 + (2.0126/2)*10^2 - 0.4553*10`

- Press
**Enter**to see the result.

- We will calculate the difference between the calculations of
**F(1)**&**F(10)**to find the area under the curve. - Enter the following formula in cell
**F10**.

`=F9-F8`

- Press
**Enter**to see the result.

**Practice Workbook**

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