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0=-1 (Calculus Puzzle)
Here's a neat puzzle I've come up with/discovered... See if you can find the error/oversight.
∫tan(x) dx = ∫sin(x)/cos(x) dx = ∫sin(x)sec(x) dx
integration by parts:
u = sec(x)
du = sec(x)tan(x) dx
dv = sin(x) dx
v = -cos(x) dx
∫tan(x) dx = -cos(x)sec(x) - ∫-cos(x)sec(x)tan(x)dx
∫tan(x) dx = -1 + ∫tan(x)dx
Now subtract ∫tan(x) dx from both sides and...
0 = -1
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