Comments on What did James Stewart mean by "the line integral reduces to an ordinary single integral in this case" ?
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What did James Stewart mean by "the line integral reduces to an ordinary single integral in this case" ?
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- Please see the question in the title, in reference to the paragraph beside my two green question marks in the image below.
- How do you symbolize "the line integral reduces to an ordinary single integral in this case"?
? - From
, how exactly do you deduce ? What warrants you to drop and disregard the ? - I disagree that
for the following reasons.- You're starting with different functions. The LHS is a BIvariate function, and the RHS is a UNIvariate function.
- The left side requires you to evaluate
at . requires no evaluation!
I scanned James Stewart, Daniel Clegg, Saleem Watson's Calculus Early Transcendentals, 9 edn 2021, pp. 1132-3.
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How do you symbolize "the line integral reduces to an ordinary single integral in this case"?
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NO.
For any function with two variables,
is an "ordinary single integral" (of the function
Consider for instance,
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