Integration — Chapter Summary

Integration is the reverse process

Integration is the reverse process of differentiation. If the derivative of a function \( F(x) \) is \( f(x) \), then the integral of \( f(x) \) is \(

There are standard results for basic

There are standard results for basic functions: \( \int x^n dx = \frac{x^{n+1}}{n+1} + C \) (for \( n \neq -1 \)), \( \int \sin x \, dx = -\cos x + C

This method involves changing the variable

This method involves changing the variable to simplify the integral. For example, to evaluate \( \int \sin(2x) \, dx \), we substitute \( u = 2x \), s

This method is based on

This method is based on the product rule of differentiation and is used for integrating products of two functions. The formula is \( \int u \, dv = uv

This technique is used to integrate

This technique is used to integrate rational functions where the degree of the numerator is less than the degree of the denominator. The rational func