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Chapter 14: Q 15. (page 1154)

Evaluate the line integral of the given function over the specified curve.

鈭�cFx,y,z.drwhereFx,y,z=ex,ey,ezand C is the line segment from0,0,0to1,1,1.

Short Answer

Expert verified

鈭�cFx,y,z.dr=e3

Step by step solution

01

Given Information

The given expression isFx,y,z=ex,ey,ez

02

Simplification

This will be evaluated using triple integral

The limits are given as x1y1,z1=0,0,0and role="math" localid="1651904409797" x2,,y2,z2=1,1,1

The line integral is evaluated as
鈭�01鈭�01鈭�01Fx,y,zdxdydz=鈭�01鈭�01鈭�01exeyezdxdydz

=exeyez

Putting limits

=e1e1e1

=e3

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