Find the circulation of Bold Upper F equals 5 x Bold i plus 7 z Bold j plus 6 y Bold k around the closed path consisting of the following three curves traversed in the direction of increasing t.

The circulation of the given vector is (5/2) x² + 7yz + 6yz + C

Step-by-step explanation:

Given that F = 5xi + 7zj + 6yk

The circulation of F is given as

Integral of F. dr

dr = idx + jdy + kdz

F. dr = (5xi + 7zj + 6yk). (idx + jdy + kdz)

= 5xdx + 7zdy + 6ydz

Integral of F. dr = Integral of (5xdx + 7zdy + 6ydz)

= (5/2) x² + 7yz + 6yz + C