Integral of Products

Some simple examples of integration.

Indefinite integration is much harder than differentiation, because there are no rules for integrating the product or quotient of two functions. It often requires guesswork. The short list of rules in Theorem 1 will help, and as this course proceeds we shall add many more techniques for finding indefinite integrals.

Integration of products.

Here is a warning that may prevent some common mistakes.

Warning: The integral of the product of two functions is not equal to the product of the integrals. The same goes for quotients. That is,

Wrong:

For example,

For example

The indefinite integral can be used to solve problems of the following type. Given that a particle moves along the y-axis with velocity v = f(t), and that at a certain time t = t₀ its position is y = y₀. Find the position y as a function of t.

Elimination of the integration constant