Question

The water level of a certain body of water is changing at a rate of W(t)=3/4cos(4-t/2) inches per hour, where t represents hours since 12 a.m.

Part A: Using correct units, explain the meaning of ∫1to10 W(t)dt in terms of the context of this problem.


Part B: Write the integral that represents the number of inches that the water level changes from 7pm to midnight.


Part C: Use your calculator to evaluate your integral from Part B. Explain the meaning of the answer in terms of the context.


Part D: What is the average daily number of inches that the water level changes for this lake?

Answer 1

The answer is below

Explanation:

a) The integral
`\int\limits^(10)_(1 ) {W(t)} \, dt` means the total change in level of water in inches from 1 am to 10 am. That is the water level change measured in inches between 1 am and 10 am

b) 7 pm is represented as t = 19 hours, while midnight is represented as t = 24 hours, hence the water level change between 7 pm and midnight is:

`\int\limits^(24)_(19 ) {W(t)} \, dt\\\\`

c) Using casio calculator to evaluate the integral gives:

`\int\limits^(24)_(19 ) {W(t)} \, dt\\\\` = 2.54 inches

D) The total daily change in water level =
`\int\limits^(24)_(0 ) {W(t)} \, dt\\\\` = 0.35 inches