Integration and differential equations

Often, when attempting to solve a differential equation, we are naturally led to computing one or more integrals — after all, integration is the inverse of differentiation. Indeed, we have already solved one simple second-order differential equation by repeated integration (the one arising in the simplest falling object model, starting on page 10). Let us now briefly consider the general case where integration is immediately applicable, and also consider some practical aspects of using both the indefinite integral and the definite integral.