Find the value of the line integral ?

In summary, the speaker has been on a forum for a week and has compiled information to help with calculus. They are taking a summer class and their professor is previewing material for the fall. The speaker asks for help with a specific problem involving a line integral, which is located in a textbook. They are unsure about how to parametrize the path and ask for assistance.
  • #1
CalleighMay
36
0
Hey guys! I have been on the forum for about a week or so and have compiled a lot of information and techniques to help me understand calculus, so i really appreciate everyone's help!

I am a soon-to-be freshman in college and am taking a summer class, calculus II (took calc I in HS). This is our last week of class after our final exam so my professor is taking this time to give us a preview of what we will be learning in the fall semester in Calc III (since this is the same professor). Every Tuesday class our professor gives us a few problems from future sections and asks us to "see what we can come up with" and to work together to find solutions. The following Tuesday he asks us to discuss the problems as a class, seeing which ones of us know our stuff =P

Basically, i want to ask you guys what you think about these problems as i do them along before i have my discussion. I really want to make a lasting impression on my professor by "knowing my stuff" -to show him i can do it! All's i need is a little help! Would you guys mind giving me some help?

We are using the textbook Calculus 8th edition by Larson, Hostetler and Edwards and the problems come from the book.

The problem is on pg 1087 in chapter 15.3 in the text, number 16a and 16b ONLY. It reads:

Find the value of the line integral integral (with a C at the bottom) of F (with a dot) dr.
Then it gives integral (with c at bottom) of (2x-3y+1)dx -(3x+y-5)dy
For a) it gives a graph with the vertices's: (0,0), (4,1) and (2,3) and there is a label (c1) in the graph on the line from (0,0) to (2,3)
For b) it gives another graph with the vertices's: (0,1), (0,-1) and it gives a half-circle with an equation x=sqrt(1-y^2) and a label (C2) in the graph.

There are graphs C and D but he told us to only try a and b... If you have a copy of the book calculus 8th edition you can see the problem for yourself... if you think it's confusing here, you can only imagine how confusing it is to me lol =(

I did look at the solutions to the other odd (i cannot find answers to even ones) problems in this problem set but it's no use, I'm totally lost. He said this will eventually be important so i want to learn it now! lol

Can you guys help me? Thank you! :D
 
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  • #2
In short they are telling to find the line integral along the path connected by the vertices. What do you know about how to parametrise paths?
 
  • #3
not a clue lol
 
  • #4
Are those straight line graphs? If so, then the parametric equation of the path is simply the vector equation of a straight line. But you have do this piecewise, as in you have to parametrise it per straight line; there isn't any complete parametric representation of all the straight lines together.
 

1. What is a line integral?

A line integral is a mathematical concept used in vector calculus to calculate the total value of a function along a specific path or curve. It involves breaking down the path into small segments and calculating the value of the function at each point, then summing these values to find the total value along the path.

2. Why is it important to find the value of a line integral?

Finding the value of a line integral is important in many fields of science and engineering, as it allows us to calculate quantities such as work, energy, and flux. It also helps us to understand the behavior of vector fields and their relationships to physical systems.

3. How is the value of a line integral calculated?

The value of a line integral is calculated by first defining the path over which the integral will be evaluated. Then, the function being integrated is multiplied by a small segment of the path, and these products are summed up over the entire path. This process is known as the Riemann sum, and as the size of the path segments approaches zero, the Riemann sum approaches the exact value of the line integral.

4. What are some real-world applications of line integrals?

Line integrals are used in many areas of science and engineering, including physics, engineering, and economics. For example, in physics, line integrals are used to calculate the work done by a force along a specific path, and in economics, they can be used to calculate the total cost or revenue of a business along a given route.

5. Are there different types of line integrals?

Yes, there are two main types of line integrals: path integrals and line integrals of vector fields. Path integrals involve integrating a scalar function over a curve, while line integrals of vector fields involve integrating a vector field over a curve. These two types of line integrals have different formulas and interpretations, but they both involve calculating the total value of a function along a specific path.

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