Line integral problem! Help is greatly appreciated! Problem is in the comments. Thanks!
[Calculus 3: Line Integrals]

Question

Line integral problem! Help is greatly appreciated! Problem is in the comments. Thanks! 
[Calculus 3: Line Integrals]

aakashsudhakar · Answer

Evaluate the line integral $$\int\limits_{C}^{ } (x^2 + y^2) dx + 2xy dy$$where C is the path of the semicircular arc of the circle $$x^2 + y^2 = 81$$starting at (9,0) and ending at (-9,0) going counterclockwise.

irishboy123 · Answer

$x^2 + y^2 = 81 $

$x \, dx + y \, dy = 0$

$  y \, dy = -x \, dx$


$\implies \int\limits_{C}^{ } 81 dx + 2x \color{red}{(-x \; dx )} = \int_{ C} \; dx \quad (81  - 2x^2) $