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1 point) Use Stoke's Theorem to evaluate ∫CF⋅dr∫CF⋅dr where F(x,y,z)=xi+yj+1(x2+y2)kF(x,y,z)=xi+yj+1(x2+y2)k and CC is the boundary of the part of the paraboloid where z=81−x2−y2z=81−x2−y2 which lies above the xy-plane and CC is oriented counterclockwise when viewed from above.

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Answer:

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Step-by-step explanation:

Thinking process:

[tex]\int\limits^a_b {cF} \, .dr[/tex]

= [tex]\int\limits^a_b {x} \, dx \int\limits^a_b {x} \, dx curlFdS[/tex] by Stoke's Theorem

= [tex]\int\limits^a_b {} \, \int\limits^a_b {} \, < 12y, -12x, 0 > .< z_x,-z_y, 1 > dA\\= \int\limits^a_b {} \, \int\limits^a_b {} \, < 12y, -12x, 0 > .< 2x, 2y, 1 > dA[/tex] since z = [tex]25-x^{2} -y^{2} \\= 0[/tex]

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