So I'm about to finish my initial course on Integral Calculus when I come across this problem:
Let there be a spherical container full of water with a 2 meter radius. How much work would it take to raise this volume of water 10 meters up from the top of the container?
I can't figure out how to even write this down as a definite integral. I do know how integrating to get Work goes:
A definite integral of the force times distance.
What I don't get is how to input the sphere (x = sqrt(4 - y^2)) in the equation or how to even write it so it's a definite integral. Help is very much appreciated.