Mastering Integration by Parts

Mastering Integration by Parts

Learning Objective

At the end of the lesson, you will be able to effectively integrate using integration by parts.

What do you already know about integration by parts?

Definition

Integration by parts is a technique used to find the integral of a product of two functions.

Formula

The integration by parts formula is ∫ u dv = uv - ∫ v du.

Choosing u and dv

Choose u as the function that you differentiate and dv as the function that you integrate.

Differentiating u

Differentiate u to find du, which is the derivative of u with respect to the variable of integration.

Integrating dv

Integrate dv to find v, which is the antiderivative of dv with respect to the variable of integration.

Applying the Formula

Substitute u, du, v, and the original integral into the integration by parts formula.

Solving the Integral

Evaluate the resulting integral and simplify the expression if necessary.

Write down 3 things you learned in this lesson.

Have students enter three things they learned in this lesson. With this they can indicate their own learning efficiency of this lesson.

Write down 2 things you want to know more about.

Here, students enter two things they would like to know more about. This not only increases involvement, but also gives them more ownership.

Ask 1 question about something you haven't quite understood yet.

The students indicate here (in question form) with which part of the material they still have difficulty. For the teacher, this not only provides insight into the extent to which the students understand/master the material, but also a good starting point for the next lesson.