Using the Trapezoidal Rule and Simpson's Rule In Exercises 3-14, use the Trapezoidal Rule and Simpson’s Rule to approximate the value of the definite
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Calculus of a Single Variable
- Insect CannibalismIn certain species of flour beetles, the larvae cannibalize the unhatched eggs. In calculating the population cannibalism rate per egg, researchers need to evaluate the integral 0Ac(t)dt, where, A is the length of the larval stage and c(t) is the cannibalism rate per egg per larva of age t. The minimum value of A for the flour beetle Tribolium castaneum is 17.6 days, which is the value we will use. The function c(t) starts at day 0 with a value 0, increases linearly to the value 0.024 at day 12, and then stays constant. Source: Journal of Animal Ecology. Find the values of the integral using a. formula from geometry; b. the Fundamental Theorem of Calculus.arrow_forwardUse the differential to approximate each quantity. Then use a calculator to approximate the quantity, and give the absolute value of the difference the two results to 4decimal places. e0.002arrow_forwardOil Consumption Suppose that the rate of consumption of a natural resource is c(t), where c(t)=kert, Here t is the time in years, r is a constant, and k is the consumption in the year when t=0. In 2010, an oil company sold 1.2 billion barrels of oil. Assume that r=0.04. a. Write c(t) for the oil company, letting t=0 represent 2010. b. Set up a definite integral for the amount of oil that the company will sell in the next 10 years. c. Evaluate the definite integral of part b. d. The company has about 20 billion barrels of oil in reserve. To find the number of years that this amount will last, solve the equation 0T1.2e0.04tdt=20. e. Rework part d, assuming that r=0.02.arrow_forward
- Use the total differential to approximate each quantity. Then use a calculator to approximate the quantity, and give the absolute value of the differences in the two results to 4decimal places. 8.052+5.972arrow_forwardu need help with this problem or this material? mber to use the Academic Support resources ble on your homepage in Brightspace or he leaming modules. Evaluate the definite integrals using properties of the definite integral and the fact that f(x) dæ f (r) da = 8, and g (1) dr = 6. = -2 (a) 7f (x) da = Number (b) f (x) dz = Number (c) (f (x) – 9 (z)) da: Number er .2 (d) (2f (z) + 3g (a)) da Numberarrow_forwardEvaluate the definite integral – 15 ) dr. using Part 1 of the Fundamental Theorem of Calculus. Remember to include a "+ C" if appropriate. (1825 - 15) dz = Number 15 )dx =arrow_forward
- help with cal hw help with finding the indefinite integralsarrow_forwardEvaluate the definite integral. Use a graphing utility to verify your result. '-1 5 du u? u -2arrow_forwardDirection: Using Riemann's Sum, find the integral of the following functions: 1.) √²(2x² - 5x + 1) dx 2.) √(x³- 2x + 1) dx 3.) f 2x³ dxarrow_forward
- ed at 10:08 PM Q2 Let a be a positive constant. Use geometry and properties of integrals to evaluate exactly [² (√₁² = 1² + \a + 3t| + a) dt. -a Q3 Let f be a function defined by the graph below. In addition, suppose 6 So f(x) dx -a for a positive constant a. Fill in the blanks. Select the not need to show your work. simplify.arrow_forward|出 TA le 1,0 A graph of f(x) is shown above. Using the geometry of the graph, evaluate the definite integrals. a) f(x) dx = b) f(x) dx = c) f(x) dx = d) f(x) dx = 10 e) 3f(x) dx =arrow_forwardUse the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the given value of n. Round your answer to four decimal places and compare the results with the exact value of the definite integral. [²1-4 Trapezoidal Simpson's exact (-4-x²) dx, n = 6 Need Help? Read It Watch Itarrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage