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Old February 11th, 2013 (8:32 AM).
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Gabri Gabri is online now
The Algorithm
Silver Tier
Join Date: Oct 2006
Location: Portugal
Age: 22
Gender: Male
Posts: 3,035
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.
"Fragile are we, look to binary means
Imprint our hopes and thoughts, our futures and dreams
into a silicon cell; Life from aluminum shells
wash away this carbon plague.

Frail and weak, contorted bags of meat
Become proponents for sentience to aid the meek
Who inherited the earth and depleted its worth...
Caretakers wanted for the carbon plague."