Okay, I am having a lot of trouble, and I'm coming to the end of the school year, really trying to understand Calculus. I feel like I understand the concepts, but whenever I attempt a question, I don't even know where to begin. Sorry to just drop a question on this forum, but I really would appreciate help.
The rate at which water flows into a tank, in gallons per hour, is given by a differentiable, increasing function R of time t. The table below gives the rate as measured at various times in an 8-hour time period.
a. Use a trapezoidal sum with the four sub-intervals indicated by the data in the table to estimate integral[0 to 8](R(t)dt). Using correct units, explain the meaning of your answer in terms of water flow.
The rate at which water flows into a tank, in gallons per hour, is given by a differentiable, increasing function R of time t. The table below gives the rate as measured at various times in an 8-hour time period.
| t (hours) | 0 | 2 | 3 | 7 | 8 |
| R(t) (gallons per hour) | 1.95 | 2.5 | 2.8 | 4 | 4.26 |
a. Use a trapezoidal sum with the four sub-intervals indicated by the data in the table to estimate integral[0 to 8](R(t)dt). Using correct units, explain the meaning of your answer in terms of water flow.
b. Is there some time t, 0 < t < 8, such that R′(t) = 0? Justify your answer.
c. The rate of water flow R(t) can be estimated by W(t) = ln(t2 + 7). Use W(t) to approximate the average rate of water flow during the 8-hour time period. Indicate units of measure.