This optional reflection is intended to be used after Exam 3, after you have also received your graded exam back. Here you can reflect on how the exam went and potentially help point to some factors that were successful or unsuccessful in your studies, so that you can better prepare for future exams.

Two young mathematicians discuss what calculus is all about.

The rate that accumulated area under a curve grows is described identically by that curve.

Two young mathematicians discuss what calculus is all about.

The accumulation of a rate is given by the change in the amount.

At this point we have three ‘‘different’’ integrals.

Two students consider substitution geometrically.

We learn a new technique, called substitution, to help us solve problems involving integration.

Two young mathematicians discuss how tricky integrals are puzzles.

We explore more difficult problems involving substitution.

We give more contexts to understand integrals.

Here we’ll practice finding integration with substitution.

Here we’ll practice finding area between curves.

Here we’ll practice finding volume using integration.

This optional reflection is intended to be used before the Final Exam. Here you can plan on how you intend to study for the final. It will help you to think about how you can prepare for the exam and what resources you have at your disposal.