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Mathematics 18 Online
OpenStudy (anonymous):

true or false: A function has one and only one antiderivative

OpenStudy (anonymous):

most have none

OpenStudy (kc_kennylau):

nope, and that's exactly the reason why we put the C at the end of each integral.

OpenStudy (anonymous):

but you are supposed to say "false"

OpenStudy (kc_kennylau):

wait what

OpenStudy (anonymous):

yeah it would be false

OpenStudy (anonymous):

for the reason @kc_kennylau wrote above

OpenStudy (kc_kennylau):

but you said "most have none"?

OpenStudy (anonymous):

yes most have none if you put all functions in a hat, (a very large hat, obviously) and pick one at random, the probability that it will be integrable is zero

OpenStudy (kc_kennylau):

lolz

OpenStudy (anonymous):

less likely still is the probability that it will have a nice closed form for an anti derivative

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