Calculus › Section O · Multiple integrals › Topic O.8

Change of variables and Jacobians

The extra r in polar integrals, the substitution factor g′(t), the area of a tilted parallelogram — one determinant explains them all. Change of variables trades an awkward region for an easy one, at the price of a Jacobian.

1 · Read 2 · Flashcards (15)3 · Test your understanding (5)

In this topic

When regions fight back
The Jacobian of a transformation
Why a determinant measures area
Worked example: polar, again
Worked example: a parallelogram's area
Worked example: an integral over the parallelogram
Three dimensions, and one
Common mistakes to avoid
Key takeaways

This topic is part of Wuanberri Pro. Checking your access…

Standards: Beyond AP

← Previous topic Next topic →