Wouldn’t it be awesome if there were some useful rules for finding antiderivatives?
Good thing there are Integration Formulas!
Indefinite Integral Notation
Okay, so we already know that integration, or antidifferentiation, is nothing more than calculating the area under the curve.
We saw how to approximate the area in our study of Riemann Sums and Sigma Notation, but now it’s time to expand upon our knowledge to include Integration properties and techniques.
As we learn the basic integration rules, we will learn the difference between an indefinite integral and a definite integral.
What’s the difference, you may ask?
Sum and Difference Property of Integrals
Well, an indefinite integral represents a function and allows us to determine the relationship between the original function and its derivative. Whereas, a definite integral represents a number and identifies the area under the curve for a specified region.
While most people nowadays use the words antidifferentiation and integration interchangeably, according to Wikipedia, antidifferentiation is the process we use when we are asked to evaluate an indefinite integral; having to add a constant “C” to our answer.
Whereas integration is a way for us to find a definite integral or a numerical value.
But all in all, no matter what you call it (i.e., antidifferentiation or integration) the formulas or integration rules that you will learn in this video will show you how to get the answer you seek!
Integration Formula
To help us in learning these basic rules, we will recognize an incredible connection between derivatives and integrals.
When we differentiate we multiply and decrease the exponent by one but with integration, we will do things in reverse.
In other words, we will increase the exponent by one and divide.
Together we will practice our Integration Rules by looking at nine examples of indefinite integration and five examples dealing with definite integration.
It’s going to be fun!
Video Tutorial w/ Full Lesson & Detailed Examples
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