(c) A non-constant function f : [0, 1] → R such that f(x) > 0 for any x e [0, 1]I f(x)dx = 0. Give a complete rigorous proof for why | f(x)dr = 0 for your example.

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Give an example of such f(x) and PROVE why it works with sequences. 

(c) A non-constant function f : [0, 1] → R such that f(x) > 0 for any r E [0, 1] but
f(x)dx = 0.
Give a complete rigorous proof for why
| f(x)dr = 0
for your example.
Transcribed Image Text:(c) A non-constant function f : [0, 1] → R such that f(x) > 0 for any r E [0, 1] but f(x)dx = 0. Give a complete rigorous proof for why | f(x)dr = 0 for your example.
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