Every time you use u-sub, you're actually transforming your region into a different one with equal areapic.twitter.com/hFyRPqd9wb
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That's the point of substitution, no? That we can solve a simpler integral of the provably same value instead?
indeed! but many people don't usually get taught that you're actually transforming a region. As you can see in the animation, the fact that the areas are equal isn't obvious geometrically
