Practice Problems on Power Rule of Integration

P1: Find the integral of the function f(x) = x2 + 1/x2.

P2: Find the integral of the curve represented by the function, f(x) = √x.

P3: If p(x) = 3x2+4x+5, find an expression for ∫p(x)dx.

P4: Integrate the function f(x) = x1/3 within limits as x = 0 and x = 1.

P5: Evaluate ∫(1/√x)dx.

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

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What is Integration?

Integration is the process of finding the integral of a function....

What is Power Rule of Integration?

Power Rule of integration states that integral of a variable x raised to a power n is the same variable x raised to power (n+1) divided by the power (n+1). This is a useful relation in determining the integral of monomial, binomial and polynomial algebraic functions....

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....

Applications of Power Rule

Power Rule of Integration can be applied to find integral of various kinds of algebraic functions such as monomial functions, polynomial functions, radical functions and some type of rational functions. It is discussed in brief along with examples as follows:...

Definite Integrals Using Power Rule

Definite Integral of a function is integral of the function calculated within some specified limits called as upper limit and lower limit of integration. Power Rule of Integration can be used for finding definite integral of algebraic functions such as polynomial functions, radical functions and some type of rational functions. A general expression to find definite integral of a algebraic function with upper limit as b and a is presented as follows,...

Sample Problems on Power Rule of Integration

Problem 1: Find the integral of function, f(x) = 3x2....

Practice Problems on Power Rule of Integration

P1: Find the integral of the function f(x) = x2 + 1/x2....

FAQs on the Power Rule of Integration

What is Power Rule of Integration?...