What is the difference between Differentiation and Integration? - ProProfs Discuss

# What is the difference between Differentiation and Integration?

Asked by G. Cole, Last updated: Jan 12, 2021

#### L. Sevigny

L. Sevigny, Doctor, Las Vegas

Answered Nov 11, 2020

Differentiation is the algebraic technique of calculating the derivatives. The derivative of a role is the slope or the gradient of the curve at any given point. Differentiation calculates the curve. It is the gradient of the tangent drawn to that curve at the given point, and it is a term used in calculus to describe a unit in change or related properties.

Integration, on the other hand, is the technique of calculating either definite integral or indefinite integral. A real function of F (X) and a closed interval on the real line, the definite integral is characterized as the area between the graph of the function, the horizontal axis, and the two vertical lines at the endpoints of an interval. When a specific interval is not provided, it is known as an indefinite integral.

#### Zack

Find happiness in writing new things.

Zack , English Professor, PhD, Basel

Answered Nov 03, 2020

Differentiation is one of the methods you can use to calculate the gradient of a curve. You can also use differentiation to determine the gradient of non-linear curves. In calculus, differentiation entails the process of determining the derived function of a function. On the other hand, you can use integration to determine the area under the curve. The relationship between integration and differentiation is that they give different opposing answers. In other words, you can consider integration as the direct opposite of differentiation. It means that if you are performing differentiation, you are only reversing the process of integration. With differentiation, you can determine the volume of objects, as well as the areas of curved surfaces. On the contrary, integration can be applied to calculate instantaneous velocity. If you want to calculate the distance traveled by a function, you should consider using integration. On the contrary, differentiation will only help you to determine the speed of the function.

#### Anthony Paul Bonadio

Its kind of my job to give answers

Anthony Paul Bonadio, Teacher, MCA, PhD, Toledo

Answered Oct 21, 2020

When you say differentiation, this means that you need to think about the rate of change of a function. When you say integration, this means that you are going to accumulate the sum of a function over a certain period of time. Take note that these two are known to be inverses of each other. These two are very useful for some of the things that are done in the real world. For example, if you would like to know the amount of material that will be used to create a certain property, you need to think about differentiation and integration so that you can get the derivative. The derivative will help you know the values of the functions that you need to do.