Mean value theorem for integrals. Let me, so this is the mean, I'll just write the acronym, mean value theorem for integrals, or integration, which essentially, and to give it a slightly more formal sense, is if you have some function g, so if g is, let me actually go down a little bit, which tells us that if g of x is continuous, continuous on this closed interval, going from a to b, then there exists, then there exists a c in this interval where g of c is equal to, what is this? This is the average value of our function. There exists a c where g of c is equal to the average value of your function over the interval. This was our definition of the average value of a function. So anyway, this is just another way of saying, you might see some of the mean value theorem of integrals, and just to show you that it's really closely tied, it's using different notation, but it's usually, it's essentially the same exact idea as the mean value theorem you learned in differential calculus, but now you have different notation, and I guess you can have a slightly different interpretation. When we're thinking about it in differential calculus, we're thinking about having a point where the slope of the tangent line of the function at that point is the same as the average rate, so that's when we had our kind of differential mode, and we were kind of thinking in terms of slopes and slopes of tangent lines, and now when we're in integral mode, we're thinking much more in terms of average value, average value of the function.