Proof of Power Rule of Integration
Integration is the reverse process of differentiation and if the integral of a function F(x) is f(x), then differentiation of f(x) gives F(x). To prove power rule of integration, we must differentiate {(xn+1) / (n+1) + C} and if we get xn then power rule is proved.
= d/dx{(xn+1) / (n+1) + C}
= d/dx{(xn+1) / (n+1)} + d/dx (C)
= 1/(n+1) d/dx (xn+1) + 0 (as d/dx(c) = 0)
= 1/(n+1)[(n + 1).xn+1-1]
= xn
Thus, d/dx ((xn+1) / (n+1) + C) = xn
Hence,
∫xn dx = (xn+1) / (n+1) + C
Thus, proved.
Now, let us discuss the applications of power rule of integration as follows.
Power Rule of Integration
Power Rule of Integration is a fundamental law for finding the integrals of algebraic functions. It is used to find the integral of a variable raised to some constant power which may be positive, negative or zero except being -1.
In this article, we will discuss the power rule of integration, its mathematical representation, its applications, definite integration using the power rule, sample problems, practice problems and frequently asked questions related to the power rule of integration.
Table of Content
- What is Integration?
- What is Power Rule of Integration
- Power Rule of Integration Derivation
- Applications of Power Rule
- Definite Integrals Using Power Rule