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Old February 11th, 2013 (08:32 AM).
Katalyst Katalyst is offline
Join Date: Oct 2006
Location: Portugal
Age: 21
Gender: Male
Posts: 1,363
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.
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


Also, I should do the same as Went.
"Discard your clothes, let loose your hair
We're intertwined forever and have always been
Say the word, and I'll depart. Upon your lips dwells
Nothing but the meaning of my cause"

© i Katalyst
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