28 июл. 2020 г. · Is it really correct to call these derivations? I.e. isn't it the case that line integrals are inherently definitions? That is to say there is ...

14 сент. 2015 г. · In the Wikipedia derivation they use the Mean Value Theorem (MVT) to approximate the distance between two points of a function →r:R→Rn by ...

18 окт. 2014 г. · Can anyone refer me to, or respond with, the derivation for the integrating term in line integrals dl=drˆr+rdθˆθ+rsinθ dϕˆϕ and volume integrals ...

17 янв. 2018 г. · By the work-kinetic energy theorem, ∫→F⋅d→r is equal to the total change in kinetic energy T between the final and initial points of that path.

4 мар. 2012 г. · A line integral (with respect to arc length) can be interpreted geometrically as the area under f(x,y) along C as in the picture.

25 янв. 2020 г. · It captures the bulk of the spirit of a rigorous derivation, but there is more to the story. However, not much is lost in their description.

30 нояб. 2012 г. · By applying the definition of integration of a k-form over a manifold we should get the formula ∫baP(γ(t))dγ1dt+Q(γ(t))dγ2dt+R(γ(t))dγ3dtdt.

5 мар. 2014 г. · The easiest (though not the most elegant) definition of ∫γϕd→ℓ is via coordinates: the integral is a vector with components ∫γϕdx, ∫γϕdy, ...

31 июл. 2020 г. · If I have a vector field F=y2i−z2j+x2k, could someone please tell me how to calculate its line integral ∫F⋅dr along both C1 and C2. Thanks!

5 авг. 2015 г. · The line integral of f over curve C shows us the area which would be restricted by f if we "straightened" and "stretched" the domain curve C into a straight ...