Finding t for Parametric Equations

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In summary, To evaluate the line integral \int x^5*z*ds, we first find the parametric equations for the line segment from (0,3,5) to (4,5,7). These are x=4t, y=3+2t, and z=5+2t. The value of t can be found by plugging in the coordinates of a point on the line, such as (0,3,5), and solving for t. Once t is known, the line integral can be solved.
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Whatupdoc
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Evaluate the line integral [tex]\int x^5*z*ds[/tex] where C is the line segment from (0,3,5) to (4,5,7)

so first thing i did was found the parametric equations
the parametric equations are:
x= 4t
y= 3+2t
z= 5+2t

how do i find out what t is? i totally forgot how to do that and i can't seem to find it in the book because it's so easy they don't bother to explain it. i can solve the problem if i know what t is, so help me if you can. thanks in advance
 
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  • #2
Surely you can figure out what t is when, say, (x, y, z) = (0, 3, 5)?
 
  • #3
lol ah thanks alot, i got it
 

1. What is a line segment?

A line segment is a portion of a straight line that is bounded by two distinct endpoints.

2. How is a line segment different from a line?

A line extends infinitely in both directions, while a line segment has a finite length and is limited by two endpoints.

3. What is the notation for a line segment?

A line segment is typically denoted by two capital letters representing the endpoints, with a bar or line drawn over the letters to indicate that it is a segment. For example, "AB" or "CD" would represent line segments.

4. Can a line segment be extended?

No, a line segment cannot be extended. It is a fixed length and cannot be altered.

5. What are some examples of real-life line segments?

Examples of line segments in the real world include the sides of a rectangle, the edges of a book, or the spokes of a bicycle wheel.

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