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Suppose that we’ve already established that the derivative of an odd function is even, and vice versa. (See Problem 2.30) Something similar can be proved for integration. However, the
following is not quite right. Let 
be even, and
let 
be its indefinite integral. Then by the
fundamental theorem of calculus, 
is the derivative of 
. Since we’ve already established that the derivative of an odd function is even, we conclude that 
is odd. Find all errors in the proof.
be even, and
let be its indefinite integral. Then by the
fundamental theorem of calculus, is the derivative of . Since we’ve already established that the derivative of an odd function is even, we conclude that is odd. Find all errors in the proof.
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