Find the value of the line integral ?

[CalleighMay]

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!!!!!

[Klaynos]

To help communication it may well be worth your time learning latex... The integral you've got I think can be written as:

 

[math]\int_c \bold {F} \cdot d \bold r = \int_c (2x+3y+1)dx -(3x+y-5)dy[/math]

 

I don't have the book so if that's wrong please correct me. You can see what you need to type to get the same type of image that I got by clicking on the equation.

 

Now what you need to do is work out the limits, and then I think you can split the integral into two parts so you get:

 

[math]\int_{a,b}^{x,y} \bold {F} \cdot d \bold r = \int_{a,b}^{x,b} (2x+3y+1)dx - \int_{a,b}^{a,y} (3x+y-5)dy[/math]

 

What do you think the sensible limits might be?

 

I've not read this but the site is normally quite good...

 

http://mathworld.wolfram.com/LineIntegral.html