I have as an assignment to find the mistake in this particular proof but I can’t find what is wrong
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My professor said there is a major mistake in this proof . Regarding the image I have nothing to write except to show the exact page of the book . If there is anything I can do to help you with the image or the context feel free to ask .I'd say it's appropriate to post the image here, to be sure there are no typos. Unfortunately, this is just a little too small for me to read comfortably, and I have no motivation to read through it carefully, because the OP said nothing at all about the context, or what they have worked out. Why are we to believe there is a mistake here, as it looks like a proof in a textbook? Does the book give this as an example of some sort of subtle error, or did the teacher just say the book is wrong? Is there any hint as to what sort of error we should look for?
I suggest you should be honest and declare that you could not find anything wrong with the proof!My professor said there is a major mistake in this proof . Regarding the image I have nothing to write except to show the exact page of the book . If there is anything I can do to help you with the image or the context feel free to ask .
I’ll repost the image here because there seemed to be a problem with the resolution View attachment 19118View attachment 19119
I agree with you I should do it myself. So so far the only thing I can’t understand is the part that it takes the partial with respect to x . Why the first integral does not depend on x .furthermore I see no point in taking the partial with respect to x because the line integral is paramertised with t as a variable and as a hole is a number and the derivative of a number is 0 .I suggest you should be honest and declare that you could not find anything wrong with the proof!
If we find the mistake for you then it would not be your work. And you will get credit for our work.
On the other hand if your professor tells you about the "location" of the mistake and you still don't understand why it is a "mistake"  we can try to help your understanding.