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Chapter 14: Q 7 (page 1153)

Determine whether the vector fields that follow are conservative. If the field is conservative, find a potential function for it.

F(x,y)=y3exy2,1+2xy2exy2

Short Answer

Expert verified

The vector field is non conservative

Step by step solution

01

Step 1:Given information 

The given expression isF(x,y)=y3exy2,1+2xy2exy2

02

Step 2:Simplification  

Consider the vector field,

F(x,y)=y3exy2,1+2xy2exy2

A vector fieldF(x,y)=P(x,y)i+Q(x,y)jis conservative if and only if鈭�P鈭�y=鈭�Q鈭�x

ComparingF(x,y)=y3exy2,1+2xy2exy2withF(x,y)=P(x,y)i+Q(x,y)j

then,

P=y3exy2

Q=1+2xy2ey2

Nowcalculating鈭�P鈭�y,鈭�Q鈭�x

鈭�P鈭�y=3y2ex2+2xy4ex2

and

鈭�Q鈭�x=exy2+2y2exy2+2xy2ey2

Since,

鈭�P鈭�y鈮�鈭�Q鈭�x

The vector field is non conservative

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Most popular questions from this chapter

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