CALCULUS HOMEWOK

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MATH233 Unit 5: Integration

Individual Project Assignment: Version 2A

IMPORTANT: Please see Part b of Problem 4 below for special directions. This is mandatory.

Note: All work must be shown and explained to receive full credit.

1. Evaluate the following:

a. ∫�5𝑥4 − 2 3 𝑥2 + 2𝑥�𝑑𝑥

b. ∫� 1 √𝑥3

+ 5𝑒5𝑥�𝑑𝑥

c. ∫ 1

7𝑥−2 𝑑𝑥

d. ∫ (9𝑥2 − 8𝑥 + 1)𝑑𝑥 2 0

e. ∫ 1

(𝑥+5)3 𝑑𝑥21

2. Consider the graph below, and answer the following:

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a. Set up the definite integral to calculate the area of the shaded region on the graph, where

the red curve is the graph of the function, 𝑓(𝑥) = 0.5𝑥2 + 𝑥 + 2, 1 < 𝑥 < 5.

b. Find the area of the shaded region.

3. The velocity (in feet per second) of a moving object at various times t (in seconds) has been

recorded and is modeled by the function 𝑣(𝑡) = 9𝑡2 + 4𝑡, where the initial position is 0 feet.

a. Find the position function, s(t), where s is in feet.

b. Find the position of the object after 2 seconds.

c. Find the change in position of the object between 5 and 10 seconds.

4. Suppose that you are asked to write a program to model a city’s population growth. The growth

rate of the city is given by the following function: 𝑑𝑃 𝑑𝑥

= 200𝑥1.075

where x is the time in years from 2010. The current population of the city is 75,000.

a. Choose three values of x between 5 and 20.

b. Important: By Wednesday night at midnight, submit a Word document stating only your name and your chosen values for x in Part a. Submit this in the Unit 5 IP

submissions area. This submitted Word document will be used to determine the

Last Day of Attendance for government reporting purposes.

c. Find the function P(x) that models the population growth.

d. Complete the following table using your three chosen values of x in Part a above by

finding the population of the city for the given years.

Actual Year x Population

e. If the population of this city follows this model in the future, interpret the meaning of the

following integral:

� 200𝑥1.075𝑑𝑥 10

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5. Which intellipath Learning Nodes helped you with this assignment?