Advanced Placement Calculus 2
Applications of Definite Integrals
Chapter 8Section 5
Applications of Science and Statistics
Essential Question:How can integration be used to determine work and fluid pressure?
Student Objectives:The students will be able to adapt their knowledge of integral calculus
to model problems involving rates of change in a variety of
applications, possibly in unfamiliar contexts.
Key Ideas:
Fluid pressure
Normal probabilities
Work (revisited)
Terms:
Derivatives
Fluid pressure
Force
Normal curve
Probability
Equations:
Graphing Calculator Skills:
Perform integration by using the fnInt command
Perform integration in the graphing window.
Sample Questions
1.Find the amount of work required to lift a 500-pound barrel 100 feet. However, the barrel is leaking at a rate of 5 pounds for every 10 feet. How much work is required to lift the barrel?
2.An isosceles triangular dam (point down) is 200 feet across and 300 feet deep. The water is 50 feet from the top and the weight of water is 62.4 lbs/ft3. What is the fluid pressure on the dam.
3.What is the probability of having a test score in the range of 85 to 95 if the average score is 77 with a standard deviation of 6 points? Integrate the problem using your calculator. Write down the problem in calculus notation as well as calculator notation.
4.A conical tank is buried in the ground point down. The tank has a diameter of 50 feet at the top and is 100 feet deep. It is buried 25 feet below the ground’s surface. The tank is full of gasoline (42 lbs/ft3) and is to be pumped to a spot 3 feet above the ground’s surface through a cylindrical pipe 6 inches in diameter. How much work is required to empty the tank?
Homework: Pages 429 - 432Exercises: #5, 7, 9, 11, 13, 15, 17, 19, 23, 25, 29, and 31.
Exercises: #6, 8, 10, 14, 16, 18, 20, 22, 24, 26, 28, and 30.
Pages 434 - 437Exercises: #1, 2, 6, 8, 12, 18, 20, 29, 32, 34, 36, 37, 38, 39, 40, 42, and 44 .
Sample Questions
1.Find the amount of work required to lift a 500-pound barrel 100 feet. However, the barrel is leaking at a rate of 5 pounds for every 10 feet. How much work is required to lift the barrel?
2.An isosceles triangular dam (point down) is 200 feet across and 300 feet deep. The water is 50 feet from the top and the weight of water is 62.4 lbs/ft3. What is the fluid pressure on the dam.
3.What is the probability of having a test score in the range of 85 to 95 if the average score is 77 with a standard deviation of 6 points? Integrate the problem using your calculator. Write down the problem in calculus notation as well as calculator notation.
4.A conical tank is buried in the ground point down. The tank has a diameter of 50 feet at the top and is 100 feet deep. It is buried 25 feet below the ground’s surface. The tank is full of gasoline (42 lbs/ft3) and is to be pumped to a spot 3 feet above the ground’s surface through a cylindrical pipe 6 inches in diameter. How much work is required to empty the tank?