\int_(r) vec(F)*dvec(r)=\int_r ([x^(2) yz y^(2)-xz x^(2) y^(2)])*([cost -sint 1])dt \int_0^(\pi ) (sin^(2)t tcost)(cost) (cos^(2)t-tsint)(-sint) (sin^(2)t cos^(2)t)dt =\int_0^(\pi ) ((1)/(2)-(1)/(2)cos2t)(cost) (1)/(2)t(1 cos2t) ((1)/(2) (1)/(2)cos2t)(-sint) (1)/(2)t(1-cos2t) 1dt \int_0^(\pi ) (1)/(2)cost-(1)/(2)cos2tcost (1)/(2)t (1)/(2)tcos2t-(1)/(2)sint-(1)/(2)cos2tsint (1)/(2)t-(1)/(2)tcos2t 1dt =\int_0^(\pi ) ((1)/(2)cost-(1)/(2)sint t 1)-(1)/(4)cos3t-(1)/(4)cost-(1)/(4)sin3t (1)/(4)sintdt =\int_0^(\pi ) (1)/(4)cost-(1)/(4)sint-(1)/(4)cos3t-(1)/(4)sin3t t 1dt =[(1)/(4)sint (1)/(4)cost-(1)/(12)sin3t (1)/(12)cos3t (2)/(2)t^(2) t]_(0)^(\pi ) ->(1)/(4)sin\pi (1)/(4)cos\pi -(1)/(12)sin3\pi (1)/(12)cos3\pi (1)/(2)\pi ^(2) \pi -(1)/(4)sh0-(1)/(4)cos0 (1)/(12)sin3(0)-(1)/(12)cos3(0) =(-1)/(4)-(1)/(12) (1)/(2)\pi ^(2) \pi -(1)/(4)-(1)/(12) =(1)/(2)\pi ^(2) \pi -(2)/(3)

intr vecFdvecrintr x2 yz y2xz x2 y2cost sint 1dt int0pi sin2t tcostcost cos2ttsintsint sin2t cos2tdt int0pi 1212cos2tcost 12t1 cos2t 12 12cos2tsint 12t1cos2t 1d class=