Navigate back to the activity.

Jeff Crabill Linn-Benton CC January 2011

I love this activity because students calculate the value of two line integrals without realizing it. After the activity (usually the next day), I discuss with them what they did and show them how they calculated the value of two line integrals without ever have been told that integration can be done over any path.

During the activity, some realized that $dh$ was equal to $\vec{\nabla} f \cdot d \vec{r}$ and they predicted that the integrals would be the same.

This term something very interesting happened that I wanted to mention. Fully 100% of the groups chose not just the correct limits of integration, but also the correct ORDER for those limits. In the past, about half of the students integrate the way they are comfortable (smallest to largest) but this term, this group of students all got it right.

The next day's lecture on line integrals went very smoothly because it was clear that they understood the concept. Students were even hinting about gradient fields, potential functions, independence of path, etc so I am very excited about the rest of the term.