Power Rule Integration

Introduction: In calculus, the power rule for integration is a fundamental technique used to find the antiderivative or integral of a function that involves a power of a variable.

Understanding the Power Rule for Integration:

The power rule is applied to functions of the form f(x) = x^n, where n is a constant and not equal to -1. This rule simplifies the process of integrating polynomial functions. Formula of the Power Rule for Integration:

The formula states that the integral of x^n with respect to x is: ∫x^n dx = (x^(n+1))/(n+1) + C, where: n is the exponent in the original function. (n+1) is the new exponent after integration. (n+1) in the denominator is used to balance the equation. C represents the constant of integration. Example:

To integrate f(x) = x²: Apply the power rule: ∫x² dx = (x^(2+1))/(2+1) + C. Simplify: ∫x² dx = x³/3 + C. Key Points to Remember:

The power rule for integration is not applicable when n = -1, as it leads to a logarithmic function. Always add the constant of integration (C) when integrating indefinite integrals.