what is integration

Question

where do we use in real life

 

Answer 1

Integration is the same as the anti-derivative of a function.

 

If the derivative of 2x is 2 , then the integral of 2 is 2x.

 

 

We use integration when we want to relate two functions, or find the area under the curve at a certain point in time. 

 

When you take differential equations, you will apply a lot of derivatives and integration to find the value of the original function f(x).

Answer 2

First let's look at derivatives. The derivative of a function will evaluate the rate of change for a point in the domain of that function. When we deal with a constant rate of change, such as the slope of a line in a linear equation, it is easy to figure out how that function is changing at any given point. When we are dealing with other sorts of functions, we need to look closer and identify the rate of change on specific intervals (such as how does it change between x=1 and x=2 or more specifical between x=1.1 and x=1.2).

 

Derivatives can be applied in many contexts, such as determining maximum profits in a business model, maximum area given various parameters, or used within the context of physics.

 

Integration works backwards from the derivative to find the original function that it was derived from.

 

There are much more specific details and a lot of different methods or formulas for finding both the derivative and the integral but I wanted to share with you how I understand it (having recently been reviewing calculus). An important part of calculus is it's exploration of change rather than static situations.