Help Solve Math Term Paper Integration Error!

In summary, the conversation discusses the investigation of a problem for a math term paper. The object in question is given a linear velocity and has an opposing acceleration, causing it to come to a stop at a certain time. The conversation also mentions the use of the Fundamental Theorem of Calculus and how it relates to the velocity function and acceleration function. The questioner is unsure of where they went wrong and considers taking the absolute value of the integral of acceleration. However, they are seeking help and feedback on their thoughts and calculations.
  • #1
MrMumbleX
12
0
The following is from my investigation of a problem for my math term paper.
An object is given a certain linear velocity, v(0), has acceleration opposing its velocity, and the object comes to a stop at time = tf due to the acceleration.
d(tf) = integral from 0 to tf of v(t)dt = integral from 0 to tf of [v(0) + integral from 0 to tf of a(t)dt]dt, d(t) is distance function of time t, v(t) is velocity function of time, and a(t) is acceleration function of time.
By Fundamental Theorem of Calculus, integral from 0 to tf of a(t)dt = antiderivative of a(tf) -antiderivative of a(0)
-> Antiderivative of a(t) = v(t)
-> integral from 0 to tf of a(t)dt = v(tf) - v(0)
-> v(tf) = 0 since the cube comes to stop
-> = v(tf) - v(0) = -v(0)

So d(tf) = integral from 0 to tf of [v(0) + -v(0)]dt = 0 -> BUT d ≠ 0
BUT d = integral from 0 to tf of v(t)dt = integral from 0 to tf of [v(0) + integral from 0 to tf of a(t)dt]dt is TRUE, and integral from 0 to tf of a(t)dt = v(tf) - v(0) = -v(0) is also TRUE.

So what did I do wrong? I was thinking to take the absolute value of the integral of acceleration, but I don't see how that would make any sense.

Help PLEASE! Any thoughts and comments are also appreciated.
 
Last edited:
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  • #2
MrMumbleX said:
The following is from my investigation of a problem for my math term paper.
An object is given a certain linear velocity, v(0), has acceleration opposing its velocity, and the object comes to a stop at time = tf due to the acceleration.
d(tf) = integral from 0 to tf of v(t)dt = integral from 0 to tf of [v(0) + integral from 0 to tf of a(t)dt]dt, d(t) is distance function of time t, v(t) is velocity function of time, and a(t) is acceleration function of time.
By Fundamental Theorem of Calculus, integral from 0 to tf of a(t)dt = antiderivative of a(tf) -antiderivative of a(0)
-> Antiderivative of a(t) = v(t)
-> integral from 0 to tf of a(t)dt = v(tf) - v(0)
-> v(tf) = 0 since the cube comes to stop
-> = v(tf) - v(0) = -v(0)
Okay, the change in velocity is -v(0).

So d(tf) = integral from 0 to tf of [v(0) + -v(0)]dt = 0 -> BUT d ≠ 0
No. you integrate the velocity function from 0 to tf, Not just the final velocity which is what you are doing here.

BUT d = integral from 0 to tf of v(t)dt = integral from 0 to tf of [v(0) + integral from 0 to tf of a(t)dt]dt is TRUE, and integral from 0 to tf of a(t)dt = v(tf) - v(0) = -v(0) is also TRUE.

So what did I do wrong? I was thinking to take the absolute value of the integral of acceleration, but I don't see how that would make any sense.

Help PLEASE! Any thoughts and comments are also appreciated.
 
Last edited by a moderator:

1. What is a math term paper integration error?

A math term paper integration error refers to a mistake made while trying to integrate mathematical equations or functions. This can lead to incorrect results or solutions.

2. How can I avoid making integration errors in my math term paper?

To avoid integration errors, it is important to double check your work and use proper mathematical notation and techniques. It is also helpful to have someone else review your work for any mistakes or inconsistencies.

3. What are some common types of integration errors?

Some common types of integration errors include forgetting to use the chain rule, incorrect substitution of variables, and forgetting to add the constant of integration. Other errors may involve arithmetic mistakes or misinterpreting the problem.

4. How can I fix an integration error in my term paper?

If you have already made an integration error in your term paper, the best way to fix it is to go back and carefully review your work. Look for any mistakes or incorrect steps, and make the necessary corrections. If you are unsure how to fix the error, seek help from a math tutor or professor.

5. Can integration errors affect my overall grade in a math course?

Yes, integration errors can have a significant impact on your grade in a math course. Depending on the severity of the error, it can lead to incorrect solutions and ultimately affect your overall understanding of the material. It is important to catch and correct any integration errors to ensure accuracy and improve your grade in the course.

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