Compute the area between two functions.

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7 Replies - 668 Views - Last Post: 14 August 2011 - 06:38 PM

#1 alias120

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Compute the area between two functions.

Posted 14 August 2011 - 05:05 PM

I am self-studying out of Calculus by Tom Apostol. As the title of this topic suggests, I am computing the area between two functions. Now I understand that this is simply the difference between integrals of the larger and smaller functions. For some reason, every single time I work through this problem I am left with only two of the three terms the book says are the answer. The problem is as follows:

Compute area A(S) between functions f(x) and g(x) within the given interval.
f(x) = x^1/3
g(x) = x^1/2
Interval is [0, 2]

So I integrate both functions and then find the difference between g(x) and f(x). Every time, I get the following answer:

4[sqr(2)]/3 - 3[cub(2)]/2

Now the book says the answer is:

4[sqr(2)]/3 - 3[cub(2)]/2 + 1/6

I cannot seem to find how the extra 1/6 was arrived at. I have worked through the problem numerous times, and I am obviously missing something. Anyone mind helping me out here?

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Replies To: Compute the area between two functions.

#2 alias120

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Re: Compute the area between two functions.

Posted 14 August 2011 - 05:37 PM

I am actually going to try and scan in my work on the problem, as this might make it easier to determine where I went wrong. One second.

#3 macosxnerd101

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Re: Compute the area between two functions.

Posted 14 August 2011 - 05:38 PM

I ran that integral on Wolfram, my TI-89 and by hand. The only way the 1/6 could be included is if there was more to the problem. Perhaps there was more in the instructions?

#4 alias120

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Re: Compute the area between two functions.

Posted 14 August 2011 - 05:48 PM

Thank you for your response. I'll get right back to you, going to read through the instructions once more.

#5 alias120

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Re: Compute the area between two functions.

Posted 14 August 2011 - 06:12 PM

Alright attached are the problem and answer pages from the book. I had to throw them in a .zip folder because DIC wouldn't let me upload .xps files (Windows Document Writer). I appreciate the help, I am not sure what I am missing. The problem I am working on is problem 7.

#6 macosxnerd101

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Re: Compute the area between two functions.

Posted 14 August 2011 - 06:23 PM

I got the same answer as you did originally, and the same answer Wolfram got. I would shoot your instructor an email asking about it. I have to disagree with the answer your book provided. Sometimes when you get second order differential equations, and you have to integrate two equations, you sometimes get a constant tagged on at the end of the final answer. However, I'm not seeing anything here that would account for the 1/6.

#7 alias120

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Re: Compute the area between two functions.

Posted 14 August 2011 - 06:36 PM

I appreciate the help macosx, and I wish I had an instructor to email. I am starting school as a transfer student this upcoming spring, and I will be taking my first Calculus course. I have been self-studying in the mean time so that the material is not new. There are a couple problems that are similar to this, where the answer has a constant thrown on the end. I will have to ask my professor once I am there.

#8 macosxnerd101

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Re: Compute the area between two functions.

Posted 14 August 2011 - 06:38 PM

I would just skip over these problems, then. I think your instructor will come to the same conclusion we did, my TI-89 did, and Wolfram did.