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meriva
3 years ago
6

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 bound

ary 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.
Mathematics
1 answer:
Drupady [299]3 years ago
3 0

Answer:

0

Step-by-step explanation:

Thinking process:

\int\limits^a_b {cF} \, .dr

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

= \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 since z = 25-x^{2} -y^{2} \\= 0

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