The water consumption (in millions of liters per year) in the country A is given by r = f(t), where t is in years and t = 0 is the start of 2015. a. Write a definite integral representing the total amount of water consumed between the start of 2017 and the start of 2022. b. Since the start of 2016 (t = 1), the rate was modeled by r = =. Using a left Riemann sum with five subdivisions, find an approximate value for the definite integral in part (a). c. Compute the exact value of the definite integral in part (a) using a substitution. d. Find the error of the approximation in part (b). Do you think it was a good approximation?

The water consumption (in millions of liters per year) in the country A is given by r = f(t), where t is in years and t = 0 is the start of 2015. a. Write a definite integral representing the total amount of water consumed between the start of 2017 and the start of 2022. b. Since the start of 2016 (t = 1), the rate was modeled by r = =. Using a left Riemann sum with five subdivisions, find an approximate value for the definite integral in part (a). c. Compute the exact value of the definite integral in part (a) using a substitution. d. Find the error of the approximation in part (b). Do you think it was a good approximation?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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I can't find a reasonable a for the definite integral. Please explain how to do question like this and answer with details, thanks!

The water consumption (in millions of liters per year) in the country A is given by r = f(t), where t
is in years and t = 0) is the start of 2015.
a. Write a definite integral representing the total amount of water consumed between the start of
2017 and the start of 2022.
b. Since the start of 2016 (t = 1), the rate was modeled by r = . Using a left Riemann sum with
five subdivisions, find an approximate value for the definite integral in part (a).
c. Compute the exact value of the definite integral in part (a) using a substitution.
d. Find the error of the approximation in part (b). Do you think it was a good approximation?

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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