What is an appropriate calculus-based justification for the fact that g is positive on the interval from the closed interval from seven to 12? So the positive on the closed interval from seven to 12. So this is interesting. Let's just remind ourselves. Here we're gonna think a little bit deeper about what it means to be this definite integral from zero to x. So if we think about what happens when x is equal to seven, x is equal to seven, when x is equal to seven, or another way of thinking about it, g of seven is going to be the integral from zero to seven of f of t dt. And so the integral from zero to seven, if this was a t-axis, and once again, t is just kind of a placeholder variable to help us keep this x up here, but we're really talking about this area right over here.