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Chapter 9: Vector Calculus

Section 9.7: Conservative and Solenoidal Fields

Example 9.7.10

If ux,y,z is a scalar potential for

 

 F=2xz+y2 i+2 x yz3 j+x23yz2 k 

 

show that CF·dr=uQuP, where C is given parametrically by the equations x=1+2 t, y=2 t2t+3, z=2+t3, and P and Q are its endpoints when t=0,1, respectively.

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