2. [10 pts] Let f e C( [a, b]). Prove that if d f(x) dr = 0 C for all a &lt; c &lt; d &lt; b, then f(x) = 0 for all r e [a, b]. Does the conclusion
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# Since a< c<d <b so if we can show a and b

are bounded then f(x) = 0. And it may hold for f is Riemann integrable?

2. [10 pts] Let f e C( [a, b]). Prove that if
d
f(x) dr = 0
C
for all a &lt; c &lt; d &lt; b, then f(x) = 0 for all r e [a, b]. Does the conclusion hold if f is Riemann
integrable on [a, b]?

#### Top Answer

The first problem for continuous f can be solved using first fundamental theorem... View the full answer

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