Ashley P.

asked • 12/06/20

Riemann Integration

Define p : [0,2] --> R by (R=set of real numbers)


p(x) = x if x<=1

p(x) = 1 if x>1


Prove that p(x) is Riemann integrable.


(You may use without proof,

integrate [f(x) dx] from 0-2 = integrate [f(x) dx] from 0-1 + integrate [f(x) dx] from 1-2

Paul M.

tutor
It is not clear what is meant by "proof". Do you need to show that the integral is a sum of 2 pieces and that each piece has a convergent Riemann sum? Do you need to show that the non-differentiability at x=1 has no bearing on the answer?
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12/06/20

Ashley P.

I just need to prove the following : Define p : [0,2] --> R by (R=set of real numbers) p(x) = x if x<=1 p(x) = 1 if x>1 Prove that p(x) is Riemann integrable. We have also been given that the following can be used as a hint for proving above. You may use without proof, integrate [f(x) dx] from 0-2 = integrate [f(x) dx] from 0-1 + integrate [f(x) dx] from 1-2
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12/06/20

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