How do I solve this line integral problem with given constraints?

In summary, the conversation was about a line integral problem involving the substitution of y=(3)1/2x and the use of Green's theorem. The integral was given by int_C ( (y-z)dx+(z-x)dy+(x-y)dz ) and C was defined by (x^2)+(y^2)+(z^2)=1 and y=x(sqrt3). The person was seeking help and was grateful for any assistance.
  • #1
nizama
10
0
Hi!

I had exam today and i got one task that i am not sure how i should have made it so i hope you can help me with this one

It goes :

Find the line integral (i'm not good with using symbols so i'll do my best here)
integral by line C from (y-z)dx+(z-x)dy+(x-y)dz
int_C ( (y-z)dx+(z-x)dy+(x-y)dz )
and C is given by
(x^2)+(y^2)+(z^2)=1
y=x(sqrt3)

thanx a lot in advance and hope to hear from any of you soon
 
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  • #2
If you make the substitution y=(3)1/2x, then you get for C:

4x2+z2=1

and you get for your integrand:

((3)1/2-1)∫Czdx-xdz

I'd use Green's theorem from there.
 
  • #3
Thank you so much

i will try to work from there :)
 

What is a line integral?

A line integral is a type of integral in calculus that can be used to calculate the total value of a function along a specific path or curve. It takes into account both the magnitude and direction of the function, and is often used in physics and engineering applications.

Why is it important to find line integrals?

Finding line integrals is important because it allows us to calculate the total value of a function along a specific path. This is useful in many fields, such as physics, engineering, and finance, where we need to know the total effect of a function over a specific path.

What is the process for finding a line integral?

The process for finding a line integral involves breaking the path or curve into small segments, calculating the value of the function at each segment, and then adding up all the values to get the total line integral. This process is known as Riemann sums and can be simplified using the Fundamental Theorem of Calculus.

What are the different types of line integrals?

There are two types of line integrals: the first type is called a line integral of the first kind, which takes into account the magnitude and direction of the function. The second type is called a line integral of the second kind, which only considers the magnitude of the function. The type of line integral you use will depend on the specific problem you are trying to solve.

How can I use line integrals in real life?

Line integrals have many applications in real life, including calculating work done by a force, finding the amount of fluid flowing through a pipe, and determining the total cost of a project. Additionally, line integrals are also used in physics to calculate the path taken by a particle in a vector field and in finance to calculate the value of a financial derivative.

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