The integration trick that your mother didn't tell you about..pic.twitter.com/byPSzn4mJl
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y = a + b - x dy = -dx x = a ⇒ y = b x = b ⇒ y = a wow
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i've done affine change of variables in specific cases but this form of it is something special
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on reflection i'm not a big fan of the gven example as one that's impossible to do otherwise i don't think you need the transformation to find out that the integrand has the symmetry around its midpoint that shows that it divides the [0, pi/2] x [0, 1] rectangle in half
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