i.4.27 Curvilinear integrals

Condition: Find the curvilinear integral of the vector \( \vec{a}=\left(y z-x^{2}\right) \vec{\imath}+\left(x z-y^{2}\right) \vec{\jmath}+\left(x y-z^{2}\right) \vec{k} \quad \) along the circular arc \( x=r \cos t, y=r \sin t \), \( z=0 \), lying in the 1st octant, from the point \( M(r, 0,0) \) to the point \( N(0, r, 0) \).