The sample dataset is a graphical representation of the equation **y=sinx** ranging from **0 to pi**. The graph has a peak at **sin (pi/2)** where the corresponding **y value** is **1**. We will calculate the area of this graph.

### Method 1 – Use the Trapezoidal Rule to Calculate the Peak Area in Excel

In this method, __we will divide the curve into some smaller trapezoids__. Then, we will calculate the **area** for those trapezoids **individually** and then **add** those small areas to get the final area.

The small segments are like trapezoids. ** The smaller the segments are, the more they resemble a trapezoid**.

**Steps:**

- Go to
**D5**and insert the following formula.

`=(C5+C4)/2*(B5-B4)`

**Explanation:**

**C4 and C5**represent the lengths of the parallel lines here. These are along y-axis in the graph.- (
**B5-B4**) represents the distance between the parallel lines. They are along x-axis in the graph.

- Press
**Enter**.**Excel**will calculate the area for a trapezoid.

- Use the Fill Handle to AutoFill to
**D16**.

- Add the areas using
**the SUM function**in D18:

`=SUM(D5:D16)`

- Press
**Enter**.

**Note:** The result is not exactly **2** as it should be. That’s because we __assumed__ the segments as trapezoids, but __they are not perfect trapezoids__. Had the segments been smaller, they would have resembled trapezoids more and we would have got the result closer to **2**.

### Method 2 – Apply a Definite Integral Rule to Calculate Peak Area in Excel

**Steps:**

- We have to determine the integral form of
**sinx**. The integration of**sinx**is –**cosx**. We will ignore the constant value since our final target is to determine the definite integration of**sinx**ranging from**0 to pi**.

- The range is from
**0**to**pi**. We will calculate**-cos(0)**and**-cos(pi)**. The corresponding values are**-1**and**1**.

- Our upper limit is
**pi**and the lower limit is**0**. We will subtract**-cos(0)**from**-cos(pi)**. Go to**F9**and write down the formula

`=F8-F7`

- Hit
**Enter.**

## Things to Remember

- The equation for the area of a trapezoid is
**A = (a+b)/2 * h**.

Where, **a** and **b** are the **length of two parallel sides**

**h** is the **distance between the parallel sides**.

- The integration of
**sinx**is**-cosx** - The value for
**cos(0)**and**cos(pi)**can also be calculated using**the COS function**. Note that the**angles**are in**radian**.

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