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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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