Assume and .

Can this be simplified to ?

Or in another way, if

,

then does this hold:

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- Apr 6th 2009, 04:22 PM #1

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- Apr 6th 2009, 05:01 PM #2

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No, they can't be simplified to that, unless a(x) and f(x) are constants.

And in general, indefinite integrals aren't equal to zero as an arbitrary constant is always added to the result.

If the integral was definite, there are still a variety of reasons why it would be equal to zero:

If , with then some possibilities are:

- Apr 6th 2009, 06:37 PM #3

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- Apr 6th 2009, 06:40 PM #4

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- Apr 6th 2009, 06:42 PM #5

- Apr 6th 2009, 06:43 PM #6

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