If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Multivariable calculus>Unit 5

Lesson 9: Proof of Stokes' theorem

# Stokes' theorem proof part 1

The beginning of a proof of Stokes' theorem for a special class of surfaces. Finding the curl of our vector field. Created by Sal Khan.

## Want to join the conversation?

• At around , Sal mentions that z subscript xy = z subscript yx. Is this property called Clairaut's Theorem?
• That is Clairaut's Theorem. It states that if the partial second derivatives exist and are continuous, then the partial second derivatives are equal. This extends to higher order differentials as well.
• at , where did the unit normal vector go? or doesn't it matter?
• Sal just forgot the vector sign over the dr. Because obiously it should be a scalar product and you need two vetors in order to compute a scalar product.