(See Solution) Evaluate ∫_C(sin (x^2)-y^2) d x+(x^3+ cos y) d y+2 z d z where C is the intersection of the paraboloid z=9-x^2-y^2 and the plane z=5

Question: Evaluate

\[\int_{C}\left(\sin \left(x^{2}\right)-y^{2}\right) d x+\left(x^{3}+\cos y\right) d y+2 z d z\]

where $C$ is the intersection of the paraboloid $z=9-x^{2}-y^{2}$ and the plane $z=5$ and $\mathcal{C}$ is oriented counterclockwise when seen from above.

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(See Solution) Evaluate ∫_C(sin (x^2)-y^2) d x+(x^3+ cos y) d y+2 z d z where C is the intersection of the paraboloid z=9-x^2-y^2 and the plane z=5

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