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divergence and curl of the given vector field

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Calculate the divergence and curl of the given vector field F.

F(x,y,z)=3xi-2yj-4zk

F(x,y,z)=(x^2 e^(-z) )i+(y^3 ln⁡〖x)〗 j+(z cosh y)k

Evaluate ∫_C▒〖P(x,y)dx+Q(x,y)dy〗

P(x,y)=xy, Q(x,y)=x+y; C is part of the graph of y = x² from (-1,1) to (2,4)

Show that the given line integral is independent of path in the entire xy-plane, then calculate the value of the line integral.

∫_((0,0))^((1,1))▒〖(2x-3y)dx+(2y-3x)dy〗

∫_((0,0))^((1,-1))▒〖(e^y 〗+ye^x)dx+(e^x+xe^y )dy

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The expert calculates the divergence and curl of the given vector field F.

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Calculate the divergence and curl of the given vector field F.

1.
Divergence:
We have
Curl:
We have
Hence
2.
Divergence:
We have
Curl:
We have ...

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