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Use Stokes' Theorem to Evaluate C(xz+2y)dx+(x2+5yz)dy+(y2+z)dz\int _ { C } ( x z + 2 y ) d x + \left( x ^ { 2 } + 5 y z \right) d y + \left( y ^ { 2 } + z \right) d z

question 192

Short Answer

Use Stokes' Theorem to evaluate C(xz+2y)dx+(x2+5yz)dy+(y2+z)dz\int _ { C } ( x z + 2 y ) d x + \left( x ^ { 2 } + 5 y z \right) d y + \left( y ^ { 2 } + z \right) d z , where C is the curve of intersection of the paraboloid z=x2+5y2z = x ^ { 2 } + 5 y ^ { 2 } and the cylinder (x4)2+(y+3)2=16( x - 4 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 16 , oriented counterclockwise as viewed from above.

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