# How to Do Calculus in Excel (Differentiation and Integration)

### How to Calculate Differentiation Manually in Excel?

Steps:

• Set the differentiation equation.
`y= x``2``+7x+5`
`Dy/Dx = 2x+7`
• Use the differentiation results as a reference formula.
• We have taken several x-values and their corresponding y-values. As we have the differential formula for our equation, we can find differentiation at every x-value.

• Enter the following formula in D8:
`=2*B8+7`
• Press ENTER.
• We get differentiation for the first point, which is -1.
• Hold and drag cell D8 downwards to find differentiation for all points.

### Finding Differentiation by Formula

Steps:

The finite difference formula is given as:

`f’(x)= {f(x+h)-f(x)}/h`
• Set the value of h and find f(x+h) and f(x). From these values, we will find the differentiation of (x). We have set the value of h as 0.0001.

• Enter the following formula in E8 to find the value of x+h.

`=B8+\$D\$8`
• Hold and drag the E8 cell downwards to get all x+h values.

• To find the values of f(x+h), enter the following formula in F8:

`=E8^2+7*E8+5`
• Press ENTER.
• Hold and drag the F8 cell downwards to find all f(x+h).

• To find f’(x), enter the following formula in G8:

`=(F8-C8)/\$D\$8`
• Press Enter.
• Hold and drag the G8 cell downwards to find all f’(x).

## Finding Integration in Excel

### Calculating Integration Manually

Steps:

The integration of the equation is given as:

∫y.dx =x^3/3+(7x^2)/2+5x

• Enter the following formula in D8 and press ENTER.

`=B8^3/3+(7*B8^2)/2+5*B8`
• Hold and drag the D8 cell downwards to find integration at all points.

### Finding the Area under the Curve with Integration

Steps:

• Enter the following formula in D8 and press ENTER.

`=(B8-B7)*(C8-C7)/2`
• Hold and drag the D8 cell downwards to get all the interval areas.

• To sum up all these area intervals, we will use the SUM function. Here is the overview of the SUM function:

Click the image for a detailed view

• Use the following formula in D18:

`=SUM(D8:D17)`

## Finding a Derivative with the SLOPE function

The overview of the SLOPE function is given in the following image:

Click the image for a detailed view

Let’s find the average velocity with this in-built function.

Steps:

• Enter the following formula in C14 and press ENTER.

`=SLOPE(B5:B12,C5:C12)`
• You will get the average velocity, which is 4.74 ms-1.

## Things Should You Remember

• When finding an area under a curve, you should take as much interval as possible. The more intervals you take, the more accurate your result will be.
• The result from these procedures is not cent percent accurate. Different methods may give you different results.
• While differentiating with the finite difference method, you must take the value of h very small for more accuracy.
• Be careful while using the formulas. Especially in the case of relative and absolute referencing.

## Calculus in Excel: Knowledge Hub

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Sourav Kundu

Sourav Kundu, BSc, Naval Architecture & Marine Engineering, Bangladesh University of Engineering and Technology, is a dedicated technical content creator of the ExcelDemy project. He has a keen interest in Excel and he leverages his problem-solving skills to provide solutions on user interface with Excel. In his position as an Excel & VBA Content Developer at ExcelDemy, Sourav Kundu not only adeptly addresses challenging issues but also demonstrates enthusiasm and expertise in navigating complex situations. Apart from creating... Read Full Bio

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