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. And now what is w of eight? Well this is going to be 30 plus the definite integral from zero to eight of r of x minus d of x minus d of x dx. And lucky for us, we're allowed to use a calculator, so let's use a calculator to evaluate this.