Hi... So I've been self-teaching Calculus III and I'm currently having a hard time coping with the idea of triple integration. You know how the integrand is f(x,y,z)? isn't that the equation to represent a 4D sketch? because technically, f(x,y,z) is ANOTHER VARIABLE and therefore giving us a 4 variable equation? If you do a double integral, you would have f(x,y) and then that would be a 3 dimensional shape; therefore, I could imagine it. BUT HOW COULD I IMAGINE A 4D SHAPE?
ALSO, I'VE BEEN LEARNING THIS THROUGH NOTES ONLINE SO BEFORE YOU CONSIDER THE FIRST QUESTION, PLEASE ANSWER THIS STUPID QUESTION, WHAT DOES THE EQUATION IN THE INTEGRAND REPRESENT? I KNOW WHAT THE LIMITS REPRESENT BUT NOT THE INTEGRAND. I THOUGHT IT REPRESENTS THE SURFACE TO INTEGRATE WITH WHEN TIMES BY dxdy/dxdydz
source: http://ift.tt/1m2GPgW
I tried to look it up, they said f(x,y,z) represents the density at that point, and when it times by dydzdx, basically it's density times volume... you'll get mass?
What!? can someone explain this please?
ALSO, I'VE BEEN LEARNING THIS THROUGH NOTES ONLINE SO BEFORE YOU CONSIDER THE FIRST QUESTION, PLEASE ANSWER THIS STUPID QUESTION, WHAT DOES THE EQUATION IN THE INTEGRAND REPRESENT? I KNOW WHAT THE LIMITS REPRESENT BUT NOT THE INTEGRAND. I THOUGHT IT REPRESENTS THE SURFACE TO INTEGRATE WITH WHEN TIMES BY dxdy/dxdydz
source: http://ift.tt/1m2GPgW
I tried to look it up, they said f(x,y,z) represents the density at that point, and when it times by dydzdx, basically it's density times volume... you'll get mass?
What!? can someone explain this please?
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