Please research at least one source of information on engineering applications of integration. Important: The purpose of this assignment is for you to share your engineering expertise and teach us how integral calculus is applied in your field. Under no circumstances should you copy and paste any content from a web reference. Instead, explain these applications in your own words.

In your original post, answer the following:

Create a summary of what you found (in your own words!) and describe an example application. Keep your post clear and concise, under 500 words.

You can use any source you like, including (but not limited to) the Internet, ECPI Library Resources, and your Electric Circuits textbook. Be sure to include the citation of your source in APA format.

# Category: Calculus homework help

1. Given the demand function D(p)=100−3p^2,

Find the Elasticity of Demand at a price of $4

At this price, we would say the demand is:

Inelastic

Elastic

Unitary

Based on this, to increase revenue we should:

Raise Prices

Keep Prices Unchanged

Lower Prices

2. Given that f'(x)=−5(x−5)(x+4),

The graph of f(x)f(x) at x=3 is Select an answer increasing concave up increasing concave down decreasing concave up decreasing concave down

3. Find ∫4e^xdx

+ C

4. Find ∫(7x^6+6x^7)dx

+ C

5. Find ∫(7/x^4+4x+5)dx

+ C

6. The traffic flow rate (cars per hour) across an intersection is r(t)=200+600t−90t^2, where t is in hours, and t=0 is 6am. How many cars pass through the intersection between 6 am and 10 am?

cars

7. A company’s marginal cost function is 5/√x where x is the number of units.

Find the total cost of the first 81 units (of increasing production from x=0 to x=81)

Total cost: $

8. Evaluate the integral

∫x^3(x^4−3)^48dx

by making the substitution u=x^4−3.

+ C

NOTE: Your answer should be in terms of x and not u.

9. Evaluate the indefinite integral.

∫x^3(8+x^4)^1/2dx

+ C

10. A cell culture contains 2 thousand cells, and is growing at a rate of r(t)=10e^0.23t thousand cells per hour.

Find the total cell count after 4 hours. Give your answer accurate to at least 2 decimal places.

_thousand cells .

11. ∫4xe^6xdx = + C

12. Find ∫6x/7x+5dx

+ C

13. Sketch the region enclosed by y=4x and y=5x^2. Find the area of the region.

14. Determine the volume of the solid generated by rotating function f(x)=(36−x^2)^1/2 about the x-axis on [4,6].

Volume =

15. Suppose you deposit $1000 at 4% interest compounded continuously. Find the average value of your account during the first 2 years.

$

16. Given: (x is number of items)

Demand function: d(x)=3362√x

Supply function: s(x)=2√x

Find the equilibrium quantity: items

Find the consumers surplus at the equilibrium quantity: $

17. Given: (x is number of items)

Demand function: d(x)=3072/√x

Supply function: s(x)=3√x

Find the equilibrium quantity: items

Find the producer surplus at the equilibrium quantity: $

18. Find the accumulated present value of an investment over a 9 year period if there is a continuous money flow of $9,000 per year and the interest rate is 1% compounded continuously.

$

19. A company manufactures 2 models of MP3 players. Let x represent the number (in millions) of the first model made, and let y represent the number (in millions) of the second model made.

The company’s revenue can be modeled by the equation

R(x,y)=110x+170y−4x^2−2y^2−xy

Find the marginal revenue equations

Rx(x,y) =

Ry(x,y) =

We can achieve maximum revenue when both partial derivatives are equal to zero. Set Rx=0and Ry=0 and solve as a system of equations to the find the production levels that will maximize revenue.

Revenue will be maximized when:

x =

y =

20. An open-top rectangular box is being constructed to hold a volume of 200 in^3. The base of the box is made from a material costing 5 cents/in^2. The front of the box must be decorated, and will cost 11 cents/in^2. The remainder of the sides will cost 2 cents/in^2.

Find the dimensions that will minimize the cost of constructing this box.

Front width: in.

Depth: in.

Height: in.

1. Evaluate the integral

∫x5(x^6−10)^47dx

by making the substitution u=x^6−10.

=_+C

2. Evaluate the indefinite integral.

∫7dx/xln(8x)

=_ + C

3. Evaluate the indefinite integral.

∫x^8e^x^9dx

=_+C

4. Evaluate the indefinite integral.

∫x4(15+x^5)^1/2dx

=_+C

5. Evaluate the indefinite integral.

∫4/(t+5)^8 dt

=_+C

6. Evaluate the indefinite integral:

∫x/x^2+4 dx

=_+C

7. A cell culture contains 4 thousand cells, and is growing at a rate of r(t)=11e^0.24t thousand cells per hour.

Find the total cell count after 4 hours. Give your answer accurate to at least 2 decimal places.

_ thousand cells

8. Use integration by parts to evaluate the integral:

∫2te^tdt =

9. ∫4xe^7xdx = + C

10. Use integration by parts to evaluate the integral:

∫ln(7x−1)dx

11. Use integration by parts to evaluate the integral:

∫ln(z)√z^13dz

12. Find ∫4x/3x+2dx

=_+C

13. Integrate: ∫x/(x^4+25)^1/2dx

=_ + C

14. Find ∫(−2x^2+3/x−1/x^4+4√x)dx

=_ + C

15. Find ∫(x+4)(x−6)dx

=_ + C

16. The traffic flow rate (cars per hour) across an intersection is r(t)=400+700t−270t2r(t)=400+700t-270t^2, where t is in hours, and t=0 is 6am. How many cars pass through the intersection between 6 am and 7 am?

_cars

17. A company’s marginal cost function is 17/√x where x is the number of units.

Find the total cost of the first 36 units (of increasing production from x=0 to x=36)

Total cost: $

For any given vertical (or horizontal) stretch or shrink, is there a corresponding horizontal (or vertical) stretch or shrink which gives rise to the identical graph transformations? Explain your reasoning.

There will be a corresponding horizontal/vertical stretch/shrink because changing one will change the position of the curve based on the input entered.

Describe a process (step-by-step) in your daily life in which the order of events is important. What would happen if you switched the order?

My work day technically starts at 7A.M. but I have to change clothes after I get there, but before I can start my day. I tend to show up at least a full hour before my shift starts so that I can go over any issues the other crew had, and get a feel for how things ran. After my shift starts I immediately have to take samples and make a round. During my round I check any equipment that is running, and anything that is coming up that day. If I were to change the order that I did my first thirty minutes of my shift there is a chance that a piece of equipment could fail. If I did my round before I took my samples, the lab would not be able to get our numbers back on time, and then I wouldn’t know what changes to make to be able to keep our equipment on quality, which could lead to a loss of tons of money for the company.

Describe a process (step-by-step) in your field of study in which the order of events is important. What would happen if you switched the order?

Troubleshooting any piece of equipment, or designing new equipment, both need to start at the basics. I wouldn’t decide to use a wooden structure for something that is going to be carrying a flame for example. So knowing what order to design the equipment would help streamline the process.

For any given vertical (or horizontal) stretch or shrink, is there a corresponding horizontal (or vertical) stretch or shrink which gives rise to the identical graph transformations? Explain your reasoning. Yes, there will always be corresponding vertical or horizontal shrink because you are basically creating a mirror image of the curve just at different coordinate points on the graph. it just depends on what function you use to determine which direction the curve goes, either left or right, up or down.

Describe a process (step-by-step) in your daily life in which the order of events is important. What would happen if you switched the order? A process in my daily life would be taking my daughter to school in the morning. the first step is getting her up in the morning and getting here ready (washing her face, brushing her teeth, getting dressed), getting some breakfast, and dropping her off. If I did that backwards I’m sure the other parents at the school would wonder, why I’m bringing my sleeping child to school trying to brush her teeth and get her dressed in her classroom.

Describe a process (step-by-step) in your field of study in which the order of events is important. What would happen if you switched the order? The research and development process in the Electrical Engineering Technology (EET) field is very important. The first step is always, determining what the objective is that needs to be met, and what obstacles may prevent you from reaching those objectives. Brainstorming, and design phase would be next to create a prototype. The next step would be the testing phase which is the most important to me. This phase helps make the design safe and make sure it will actually do the job. In my opinion I don’t believe you can do this in any other order. you can’t test something that hasn’t been designed or built. Or you can’t design something without knowing what the objective of the design is or knowing what issue you may run into because of the objective you are trying to reach.

For any given vertical (or horizontal) stretch or shrink, is there a corresponding horizontal (or vertical) stretch or shrink which gives rise to the identical graph transformations? Explain your reasoning.

There will be a corresponding horizontal/vertical stretch/shrink because changing one will change the position of the curve based on the input entered.

Describe a process (step-by-step) in your daily life in which the order of events is important. What would happen if you switched the order?

My work day technically starts at 7A.M. but I have to change clothes after I get there, but before I can start my day. I tend to show up at least a full hour before my shift starts so that I can go over any issues the other crew had, and get a feel for how things ran. After my shift starts I immediately have to take samples and make a round. During my round I check any equipment that is running, and anything that is coming up that day. If I were to change the order that I did my first thirty minutes of my shift there is a chance that a piece of equipment could fail. If I did my round before I took my samples, the lab would not be able to get our numbers back on time, and then I wouldn’t know what changes to make to be able to keep our equipment on quality, which could lead to a loss of tons of money for the company.

Describe a process (step-by-step) in your field of study in which the order of events is important. What would happen if you switched the order?

Troubleshooting any piece of equipment, or designing new equipment, both need to start at the basics. I wouldn’t decide to use a wooden structure for something that is going to be carrying a flame for example. So knowing what order to design the equipment would help streamline the process.

For any given vertical (or horizontal) stretch or shrink, is there a corresponding horizontal (or vertical) stretch or shrink which gives rise to the identical graph transformations? Explain your reasoning. Yes, there will always be corresponding vertical or horizontal shrink because you are basically creating a mirror image of the curve just at different coordinate points on the graph. it just depends on what function you use to determine which direction the curve goes, either left or right, up or down.

Describe a process (step-by-step) in your daily life in which the order of events is important. What would happen if you switched the order? A process in my daily life would be taking my daughter to school in the morning. the first step is getting her up in the morning and getting here ready (washing her face, brushing her teeth, getting dressed), getting some breakfast, and dropping her off. If I did that backwards I’m sure the other parents at the school would wonder, why I’m bringing my sleeping child to school trying to brush her teeth and get her dressed in her classroom.

Describe a process (step-by-step) in your field of study in which the order of events is important. What would happen if you switched the order? The research and development process in the Electrical Engineering Technology (EET) field is very important. The first step is always, determining what the objective is that needs to be met, and what obstacles may prevent you from reaching those objectives. Brainstorming, and design phase would be next to create a prototype. The next step would be the testing phase which is the most important to me. This phase helps make the design safe and make sure it will actually do the job. In my opinion I don’t believe you can do this in any other order. you can’t test something that hasn’t been designed or built. Or you can’t design something without knowing what the objective of the design is or knowing what issue you may run into because of the objective you are trying to reach.