Download Presentation
## ATHS

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**ATHS**Calculus Project Grade: 12 – ES**GOALS**• Students will interpret their understanding of applications of integration • Students will use technology for research and communication: wiki/blog. • Students will present their findings to the class through digital Media(Video/Booklet).**Theme /INTRO**• This project covers the application of topics in calculus; students will apply the concepts and theorems they have learned on integration. Moreover students will be able to apply their knowledge in relation to vari**TASK 1**• The boundaries of a piece of land that belongs to your family can be best described as in the following graph: • i.e. the area between the 𝑥−axis and the graph of the function 𝑓(𝑥)=𝑥3 − 5𝑥2 +6𝑥+5**Answer the following questions:**• 1. Using approximating rectangles dividing the interval from 0 to 4 into 5 equal subdivisions, estimate the area between f(𝑥)= 𝑥3 − 5𝑥2 +6𝑥+5 and the 𝑥−axis, with ∆x=0.8 .**2. Calculate the exact value of the same area using the**definite integral.**Task 2”Oil Consumption”**• Suppose that the rate of consumption of a natural resource is 𝑐′(𝑡), where: 𝑐′(𝑡) = 𝑘𝑒𝑟𝑡. • Here 𝑡 is time in years, 𝑟 is a constant, and 𝑘 is the consumption in the year when 𝑡 = 0. In 2006, an oil company sold 1.2 billion barrels of oil. Assume that 𝑟=0.04.**b) Set up a definite integral for the amount of oil that the**company will sell in the next 10 years.**d) The company has about 20 billions barrels of oil in**reserve. To find the number of years that this amount will last, solve the equation:**Task 3**• The annual revenue for your company over the past five years was found to follow the following Integral formula: Where n is the number of years**1. Verify the following relation between two consecutive**years' revenue:**Task 4**• A water well of depth 50 feet is used to supply people with water. A rope of weight 0.2 lbs/ft is used take the water out of the well using a barrel that weight 80 lbs when it is full of water.**a) Calculate the work needed to lift the barrel from the**bottom to the midpoint of the well.**b) Calculate the work needed to lift the barrel from the**midpoint of the well to the top of the well.