Line integral and parametrization

In summary, the conversation is about the correct parametrization and limits for solving an integral problem involving a curve connecting two points. The correct answer is 7 and the parametrization given is (1, 1+t, 1+3t). The person asking the question realizes their mistake and admits it.
  • #1
Tony11235
255
0
I know this is dumb question but for some reason I have not been able to get the right answer to the following problem:

[tex]\int_{c} 2xyzdx+x^2 zdy+x^2 ydz [/tex]

where C is a curve connecting (1, 1, 1) to (1, 2, 4).

My parametrization is (1, 1+t, 1+3t). My limits are the problem...I think. By the way the correct in answer in the book is 7.
 
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  • #2
Tony11235 said:
I know this is dumb question but for some reason I have not been able to get the right answer to the following problem:

[tex]\int_{c} 2xyzdx+x^2 zdy+x^2 ydz [/tex]

where C is a curve connecting (1, 1, 1) to (1, 2, 4).

My parametrization is (1, 1+t, 1+3t). My limits are the problem...I think. By the way the correct in answer in the book is 7.

Your parametrization is fine. You said your limits are the problem, but which are you using? Which value t would give your first point? The second?

Alex
 
  • #3
OMG...I am retarted. :bugeye:
 

What is a line integral?

A line integral is a type of integral that calculates the total value of a function along a given curve or path in a multi-dimensional space. It is used to measure the work done or the amount of a physical quantity, such as force or energy, along a specific path.

What is parametrization?

Parametrization is the process of representing a curve or surface in terms of one or more parameters. It allows us to describe a complex shape or path using a simpler mathematical function that can be easily manipulated and analyzed.

How is a line integral calculated?

A line integral is calculated by breaking up the given curve or path into small segments, approximating the function at each segment, and then adding up the values of the function at each point. This is similar to how a regular integral is calculated, but instead of integrating over a single variable, we integrate over the parameter(s) that define the curve or path.

What is the significance of line integrals?

Line integrals have various important applications in physics, engineering, and mathematics. They can be used to calculate work done by a force, find the mass of an object, determine the center of mass of a system, and analyze electric and magnetic fields, among others.

What is the difference between a line integral and a surface integral?

A line integral is calculated over a one-dimensional curve or path, while a surface integral is calculated over a two-dimensional surface. Line integrals are also known as path integrals, while surface integrals are also known as area integrals.

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