Evaluate in the (x,y)-plane the line integral F.dr, where F=(3xy, -y^2) and C is the curve given by y=2(x^2)?

(10x - 3x^2 - 3y^2) dy dx. Since the region enclosed by C is a sector of a circle (with 45 degrees), we convert to polar coordinates:?(? = 0 to? /4)?(r = 0 to 4) (10r cos?

- 3r^2) * (r dr d?)?(? = 0 to? /4)?(r = 0 to 4) (10r^2 cos? - 3r^3) dr d?(? = 0 to?

/4) (10/3)r^3 cos? - (3/4)r^4 {for r = 0 to 4} d?(? = 0 to? /4) (640/3) cos?

- 192 d? (640/3) sin? - 192?

{for? = 0 to? /4} (320/3)?2 - 48?.

I hope this helps!

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