- #1

thaiqi

- 160

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- TL;DR Summary
- wondering about a proof of exchange between variation sign and integral sign

Hello, everyone.

I know that it is feasible to exchange the order of one variation sign and one integral sign. But there gives a proof of this in one book. I wonder about a step in it. As below marked in the red

rectangle:

How can ##\delta y## and ##\delta y^\prime## be moved into the integral sign? Aren't they functions of ## x ## ?

I know that it is feasible to exchange the order of one variation sign and one integral sign. But there gives a proof of this in one book. I wonder about a step in it. As below marked in the red

rectangle:

How can ##\delta y## and ##\delta y^\prime## be moved into the integral sign? Aren't they functions of ## x ## ?