So I was given the following question:
"The sum $\sum_{k=1}^n h'(\frac{15}{n}(k-1))\frac{15}{n}$ is a left Riemann sum with $n$ sub intervals of equal length. The limit of this sum as $n$ goes to infinity can be interpreted as a definite integral. Express the limit as a definite integral."
The following table was given with the question:
I know the conversion to an integral looks something like this: $\int_a^b f(x)dx=\lim_{n \to \infty} \sum_{i=1}^n f(x_i)*\Delta x_i$
I figured out that the upper limit of this definite integral must be $15$ and that the lower should be $0$, but I'm a bit confused on what the actual function would look like. Any help would be appreciated!
Edit: I was also given the following information: "the height of water in a storage tank during a $15$-hour period is given by a twice-differentiable function $h$, where $h(t)$ is measured in feet and $t$ is measured in hours since midnight for $0<t<15$. The graph of $h$ is concave up on the interval $0<t<15$. Selected values of the derivative of $h$,$h'(t)$, are given in the table above. At time $t=2$, the height of the water is $7$ feet."