Compute Line Integral: (x/y) from (2,4) to (10,100)

In summary, a line integral is a mathematical operation in vector calculus that involves finding the integral of a scalar or vector function along a specified curve or path. It can be interpreted as finding the area under the curve or the work done along the path. The formula for computing a line integral is ∫<sub>a</sub><sup>b</sup> F(x,y) • dr, where F(x,y) is the vector-valued function and dr is the differential of the curve or path. Some real-world applications of line integrals include calculating work, circulation, and flux in various fields such as physics and engineering.
  • #1
balrog1212
3
0
The question is compute the integral over c of (x/y) where c is the line segment from (2,4) to (5, 25) followed by the parabolic arc from (5, 25) to (10, 100)

I tried setting this up in terms of x and then y using the line integral formula but I am got a negative answer which i know can't be right. Can anyone help me set this up?
 
Mathematics news on Phys.org
  • #2
What do you have for the function, it's derivative, and the integral?
 
  • #3
There are many different ways to do such a problem. Show us what you did and we may be able to help.
 

FAQ: Compute Line Integral: (x/y) from (2,4) to (10,100)

What is a line integral?

A line integral is a type of mathematical operation performed in vector calculus that involves calculating the integral of a scalar or vector function along a specified curve or path.

What does it mean to compute a line integral?

To compute a line integral, you are finding the area under a curve or the work done along a path by summing up infinitesimal contributions from the curve or path.

What is the formula for computing a line integral?

The formula for computing a line integral is: ∫ab F(x,y) • dr where F(x,y) is the vector-valued function and dr is the differential of the curve or path.

How do you interpret the integral of (x/y) from (2,4) to (10,100)?

The integral of (x/y) from (2,4) to (10,100) represents the total area under the curve of the function (x/y) between the points (2,4) and (10,100). This can also be interpreted as the work done along the curve from (2,4) to (10,100).

What are some real-world applications of computing line integrals?

Line integrals have many applications in physics, engineering, and other fields. They can be used to calculate the work done by a force along a path, the circulation of a fluid, and the flux of a vector field. They also have applications in electromagnetism and fluid mechanics.

Similar threads

MHB Mechanics- general motion in a straight line.
Replies
2
Views
1K
I Volume of Solid of Revolution (About the line y = x)
Replies
6
Views
1K
MHB How do I sketch the reflection of line segment AB about the line y = x?
Replies
5
Views
2K
MHB #s of Combinations and Permutations of lines?
Replies
1
Views
926
MHB 2.4.10 3 circles one intersection
Replies
8
Views
1K
MHB Luca's question via email about a line integral....
Replies
2
Views
5K
Line Integral: Computing for $\int _1 ^2 V(x)dx$
Replies
2
Views
2K
Verify Green's Theorem in the given problem
Replies
10
Views
1K
MHB Reflecting B(3,-1) on Line g: 4y + x - 15 = 0
Replies
3
Views
1K
MHB Find an equation of the line that is perpendicular to x - y + 2 = 0
Replies
5
Views
1K

Hot Threads

Recent Insights

Back
Top