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Finding line integrals to be a bit boring? Well, this tutorial will add new dimension to your life by explore what surface integrals are and how we can calculate them.
Partial Derivatives of Vector-Valued Functions
Introduction to the surface integral
Example of calculating a surface integral part 1
Example of calculating a surface integral part 2
Example of calculating a surface integral part 3
Visualizing a suitable parameterization
Taking the cross product to calculate the surface differential in terms of the parameters
Using a few trigonometric identities to finally calculate the value of the surface integral
Parametrizing a surface that can be explictly made a function of x and y.
Evaluating the surface integral
Breaking apart a larger surface into its components
Evaluating the surface integral over the outside of the chopped cylinder
Parametrizing the top surface
Evaluating the third surface integral and coming to the final answer