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Randolph College
Department of Mathematics and Computer Science

 

Homework # 22 - Math 250


The problems on this homework must be done alone.  The honor code is in effect.

 First name:   Last name:


 

1.  Say C1:r1(t),atb, and C2:r2(t),ctd are two piecewise smooth curves such that r2(c)=r1(a), and r2(d)=r1(b). Is it true that C2Fdr=C2Fdr?

a.  Definitely yes.

b.  Definitely no.

a.  It could possibly happen.

 

2.  Say C1:r1(t),atb, and C2:r2(t),ctd are two piecewise smooth curves such that r2(c)=r1(a), and r2(d)=r1(b), and F is conservative. Is it true that C2Fdr=C2Fdr?

a.  Definitely yes.

b.  Definitely no.

a.  It could possibly happen.

 

3.  Evaluate Cx+y,xydr, where C is the path that starts at (0,0), goes in a straight line to (1,1), then goes in a straight line to (3,-1), then goes in a straight line to (5, 1), and then goes in a straight line to (6,0). (Hint: if you're working hard on this one, you're working too hard.)

a.  12

b.  16

a.  18

b.  24

b.  30