Math Problem Solver

Use Stoke’s theorem to evaluate ∮ 𝐹⃗.𝑑𝑟⃗

𝐶

where 𝐹⃗ = (2𝑥 −𝑦)𝑖̂−𝑦𝑧2𝑗̂−

𝑦2𝑧𝑘 ̂ and 𝐶 is the boundary of the surface 𝜎 which is the upper half of the

sphere 𝑥2 + 𝑦2 +𝑧2 = 1 oriented upwards.