Is paramitric Equation Correct?

[m_s_a]

Homework Statement

http://up5.m5zn.com/photos/00017/t4x1262r70cu.jpg[/URL]
http://up5.m5zn.com/photos/00017/rpbn4bsfcace.jpg[/URL]

Homework Equations

The Attempt at a Solution

C1:z(t)=t , 0<t<5
C1:z(t)=5+it , 0<t<5
C2:z(t)=1-t+5i , 0<t<5
C3:z(t)=5-t+5i , 0<t<5
C4:z(t)=i(1-t) , 0<t<5
Is paramitric Equation Correct?

 

[Dick]

1) Not really any difference as far as I know. They both indicate integral over the contour C. 2) The parametric form for the contour has several mistakes. Can you find one? I'll get you started. The contour has 4 segments, you've listed 5. Two of them labelled C1. What's up with that?

 

[m_s_a]

Dear
Dick
مرحبا
سعيد يرؤيتك
1)
I can not find an answer in books,In books sometimes use pattern,Sometimes using type IIusing
In your answer:
They both indicate integral over the contour
Do you clarify if possible
2)

C1:z(t)=t , 0=<t=<5
C2:z(t)=5-t+5i , 0=<t=<5
C3:z(t)=5-t+5i , 0=<t=<5
C4:z(t)=i(5-t) , 0=<t=<5
Sorry for error
I will try again.
Thanks
See you

 

[HallsofIvy]

For (1), IF "C" represents the same contour in both integrals, then, as Dick said, they are the same. However, I suspect that the question did not mean to imply that. If the two different "C"s may mean different contours, then the first form implies that C is a closed contour while the second does not.


For (2), now you've got C2 and C3 exactly the same! (Your second "C1" in your first answer should have been "C2".)

 

[m_s_a]

Hi king
O.K.
used (I) for Contour = sum of Curves , and Closed
and used (II) for any Curve

Q.2
Now
z1(t)=t , 0=<t=<5
z2(t)=5+it , 0=<t=<5
z3(t)= t+5i , 5=<t=<0
z4(t)=it , 5=<t=<0