Example 2 Let F(x, y) = -y7 +23. Find the line integral of Falong the given path. (a) C₁ is the quarter of unit circle 2

Post by **answerhappygod** » Wed Jul 06, 2022 12:32 pm

: Example 2 Let F X Y Y7 23 Find The Line Integral Of Falong The Given Path A C Is The Quarter Of Unit Circle 2 1 (19.92 KiB) Viewed 14 times

Please ONLY do Remark #2 and answer the following questions:
Parameterize the given C in two different ways to evaluate the line integral. Verify that the line integral does NOT depend on the choice of parameterization.
Thank you!
Example 2 Let F(x, y) = -y7 +23. Find the line integral of Falong the given path. (a) C₁ is the quarter of unit circle 2² + y² = 1 in the first quadrant, oriented counterclockwise. (b) C₂ is the line segment from (1,0) to (0, 1). (c) C3 is a path from (1,0) to (0, 2) along the parabola y = 2-2r²,
Remarks (1) The line integral of F along C can also be denoted using the differential notation. ofF.d7 does (2) As discussed above, the parameterization for C is not unique. The result of NOT depend on the parameterization chosen. (Text 18.2/34)