And we can use any variable we want, it's really just a bit of a placeholder variable for the integration. So our net inflow is r, I'll say r of x, minus d of x, and then dx. Once again, this is our net rate of inflow, this is our inflow minus our outflow, so our net rate of inflow times small changes, you could view this as time, although it's x, and then we sum up from zero to time is equal to t. So this is how much water we are going to have in the pipe at any time t. So let's now think about at what point does w hit a minimum in this interval? And there's three possibilities where w could hit a minimum point. It could hit a minimum right at the beginning, at w of zero, it could hit it at the end of our interval, at w of eight, at t equals eight, or it could be someplace in between where w is at a local maximum point, in which case the derivative of w will be equal to zero. So let's first evaluate w at the end points. So w of zero, well we know that, that's the bounds are gonna be zero to zero, they even gave that to us in the problem, is the initial state is we have 30 cubic feet of water in the pipe already.