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What did James Stewart mean by "the line integral reduces to an ordinary single integral in this case" ?

~~1. Please see the question in the title, in reference to the para. aside my two green question marks below.~~
~~2. How do you symbolize _"the line integral reduces to an ordinary single integral in this case"_? $\int^b_a f(x {\color{goldenrod}{, 0)}} \, dx = \int^b_a f(x) \, dx $?~~
~~2. From $\int^b_a f(x \color{goldenrod}{, 0)} \, dx $, how exactly do you deduce $= \int^b_a f(x) \, dx$? What warrants you to drop and disregard the $\color{goldenrod}{, 0)}$?~~
~~4. I disagree that $\int^b_a f(x {\color{goldenrod}{, 0)}} \, dx = \int^b_a f(x) \, dx $ for these reasons.~~
~~4.1. You're starting with different functions. The LHS is a BIvariate function, and the RHS is a UNIvariate function.~~
4.2. The left side requires you to evaluate $f(x, y)$ at $y = 0$. $f(x)$ requires no evaluation!
I scanned James Stewart, Daniel Clegg, Saleem Watson's *Calculus Early Transcendentals*, 9 edn 2021, pp. 1132-3.
~~![Image alt text](https://math.codidact.com/uploads/ldkzpx36gacjpg6irobvevgryitl)~~

1. Please see the question in the title, in reference to the paragraph beside my two green question marks in the image below.
1. How do you symbolize _"the line integral reduces to an ordinary single integral in this case"_? $\int^b_a f(x {\color{goldenrod}{, 0)}} \, dx = \int^b_a f(x) \, dx $?
1. From $\int^b_a f(x \color{goldenrod}{, 0)} \, dx $, how exactly do you deduce $= \int^b_a f(x) \, dx$? What warrants you to drop and disregard the $\color{goldenrod}{, 0)}$?
1. I disagree that $\int^b_a f(x {\color{goldenrod}{, 0)}} \, dx = \int^b_a f(x) \, dx $ for the following reasons.
1. You're starting with different functions. The LHS is a BIvariate function, and the RHS is a UNIvariate function.
1. The left side requires you to evaluate $f(x, y)$ at $y = 0$. $f(x)$ requires no evaluation!
I scanned James Stewart, Daniel Clegg, Saleem Watson's *Calculus Early Transcendentals*, 9 edn 2021, pp. 1132-3.
![Pages 1132 and 1133 of Calculus Early Transcendentals](https://math.codidact.com/uploads/ldkzpx36gacjpg6irobvevgryitl)

line-integral