8 мар. 2014 г. · The line integral is basically like the ordinary integral: it "adds up" how much stuff you collect as you move through some sort of "field" of a ...

4 сент. 2024 г. · A path integral over a vector field is summing up all the components of the vectors along a path that point in the same direction as that path.

16 авг. 2024 г. · The simplest way is to treat the two outputs separately. That is, f(x,y) = (z,w), then separately integrate over the curve (integral of the ...

27 апр. 2014 г. · In other words, the integrals along the two paths are equal. So the line integral does not depend on which path you take, only the end points.

8 окт. 2020 г. · One key property of integrals in general is that you can break them up, calculate them individually, and then add the results. In terms of ...

1 дек. 2020 г. · A line integral is the sum of all vectors in a vector field along a path. The vector is expressed as F. What about the path, how do you express ...

16 авг. 2022 г. · Geometrically, you can think of a line integral as measuring the area of a "ribbon" underneath a 2-(or more)-d function. Alternatively, you can ...

24 нояб. 2019 г. · We know that the line integral of a 3D scalar function is the area of the "curtain" underneath the function over some 2D curve. Then, if we know ...

25 апр. 2024 г. · You combine the two equations to get the equation for the intersection. I think the best way is to complete the square so you get an ellipse equation.

31 мар. 2023 г. · For a flat surface a surface integral gives the surface area of a curve. For a non flat surface a line integral gives the area under a curve.