- Integration by Parts by M. Bourne Sometimes we meet an integration that is the product of 2 functions. We may be able to integrate such products by using Integration by Parts. If u and v are functions of x, the product rule for differentiation that we met earlier gives us: d d x (u v) = u d v d x + v d u d x
In the last section, we learned how to reverse the chain rule. How do we reverse other rules of differentiation? In this section, we’ll tackle this question for the product rule of differentiation. What is the method of integration by parts and how can we consistently apply it to integrate products of basic functions?
Integration by Parts # How to Integrate Products of Different Types of Functions # Reversing the Product Rule of Differentiation The product rule for differentiating f (x) g (x) (i.e., d d x (f g) = f ′ g + f g ′) can be translated into the following rule for computing the antiderivative of a product: ∫ f g ′ d x = f g ∫ f ′ g d x
Theoretically, if an integral is too "difficult" to do, applying the method of integration by parts will transform this integral (left-hand side of equation) into the difference of the product of two functions and a new ``easier" integral (right-hand side of equation). It is assumed that you are familiar with the following rules of differentiation.
Differentiation The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity. The laws of Differential Calculus were laid by Sir Isaac Newton. The principles of limits and derivatives are used in many disciplines of science. Differentiation and integration form the major concepts of ...