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sin(1/x) riemann integrable
Is the function from [0,1] to R defined by
f(x) = 0 if x = 0
f(x) = if
riemann integrable? how to prove/disprove it?
Cheers,
D
f(x) = 0 if x = 0
f(x) = if
riemann integrable? how to prove/disprove it?
Cheers,
D
Don't actually try to construct a dissection.
Use the Riemann criterion for integrability, and split your original integral into two parts: one from 0 to epsilon and another from epsilon to 1.
Note that for any interval [epsilon, 1] sin(1/x) is continuous, and you can bound the other bit.
Use the Riemann criterion for integrability, and split your original integral into two parts: one from 0 to epsilon and another from epsilon to 1.
Note that for any interval [epsilon, 1] sin(1/x) is continuous, and you can bound the other bit.
Related discussions
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