Calculus Homework Help Needed ASAP

Page 1 of 2

MATH233 Unit 5: Integration

Individual Project Assignment: Version 2A

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 𝑑𝑥

2

1

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

Page 2 of 2

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

c. 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

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

following integral:

∫ 200𝑥1.075𝑑𝑥 10

5

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