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Evaluate $\int _ { C } \sqrt { x + 2 y } d s ,$ where $C$ is

a. the straight-line segment $x = t , y = 4 t ,$ from $( 0,0 )$ to $( 1,4 )$ .

b. $C _ { 1 } \cup C _ { 2 } ; C _ { 1 }$ is the line segment from $( 0,0 )$ to $( 1,0 )$ and $C _ { 2 }$ is

the line segment from $( 1,0 )$ to $( 1,2 )$ .

A. $2 \sqrt{17}$

B. $2 \sqrt{17}[1+2 \sqrt{2}]$

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University of Illinois at Urbana-Champaign