How do i solve this integral?

  • Thread starter iScience
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  • #1
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if i have a function U..

U=∫F∙ds

where F=<ayz+bx+c , axz+bz , axy+by> , a,b,c are constants

so.. F=(ayz+bx+c)[itex]\hat{x}[/itex] + (axz+bz)[itex]\hat{y}[/itex] + (axy+by)[itex]\hat{z}[/itex]

then how do i solve this integral? i have to either replace the x,y,z terms with something in terms of 's' (which is the displacement by the way, ie.. s= [itex]\sqrt{x^2+y^2+z^2}[/itex]
or i have to replace ds with some parametric ..stuff... how do i evaluate something like this?
 
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  • #2
tiny-tim
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Hi iScience! :smile:
U=∫F∙ds

or i have to replace ds with some parametric ..stuff... how do i evaluate something like this?
Let's write that out in full …

it's an integral over a curve C between two endpoints P1 and P2: ##U = \int_C \mathbf{F}\cdot d\mathbf{s}##

so yes you have to use some parameter, which may be s itself, or may be something easier to use, eg θ with ds = (-rsinθdθ,rcosθdθ) :wink:
 

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