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Old February 11th, 2013 (8:32 AM).
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Katalyst Katalyst is offline
Do the Toxic Waltz
 
Join Date: Oct 2006
Location: Portugal
Age: 22
Gender: Male
Posts: 2,365
If you can do simple math, tell me what is the integral of F·dr (dot product between the vectors F and dr), where F is the vectorial function whose coordinates are given by (10x^4 - 2x*y^3 ; -3x^2*y^2) and dr is the position differential vector of coordinates (dx; dy) along the path given by x^4 - 6x*y^3=4y^2, from the starting point (0;0) to the final point (2;1).

It's quite simple actually.
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The curl of the function F is zero (d/dy (10x^4 - 2x*y^3) = -6x*y^2 = d/dx (-3x^2*y^2)), and as such the path you integrate the function along doesn't matter. Find the scalar function G whose derivative with respect to x is the first coordinate of F and whose derivative with respect to y is the second coordinate of F ---> G=2x^5 - x^2*y^3. Just do G(2;1)-G(0,0) and done! The final result is 60.


Blaarh, I tried to translate the names of that stuff as best as I could.

/end show-off

216798

Also, I should do the same as Went.
"Is it my face you see? Do I haunt you in your sleep,
on your hands and knees, when you crawl through your nightmares?
When there's no more grace... does your heartbeat start to race?
Clawing everywhere, in the dark poisonous shadows"

© i Katalyst