Tutoring a student on integrals; I think the textbook's answer is wrong

[ksdhart2]

Hi all. So I'm tutoring a student on another forum and I've found a problem that's given me some grief. I think there might be an error in the problem somewhere, and I just want to make sure I'm not going crazy or missing something obvious. The full text of the problem is:

97. If \(\displaystyle \int f(x) \: dx = 4\) and \(\displaystyle \int g(x) \: dx = 2\), find \(\displaystyle \int \left[ 3f(x) + 2g(x) + 1 \right] \: dx\)

By the sum and constant multiple rules, it's trivial to get it down to:

\(\displaystyle 3(4) + 2(2) + \int 1 \: dx\)

But wouldn't this necessarily have to produce an answer of 16 + x + C? The given answer choices were:

• A: 23
• B: 22
• C: 25
• D: 24

and answer B is indicated with an asterisk as the correct one. According to the student, there's no previous information about the value of x or about how to narrow down what the constant of integration might be.

 

[MarkFL]

To me, a statement like:

[MATH]\int f(x)\,dx=4[/MATH]
is meaningless...there needs to be limits, i.e., a definite integral.

 

[Steven G]

To me, a statement like:

[MATH]\int f(x)\,dx=4[/MATH]
is meaningless...there needs to be limits, i.e., a definite integral.

What you said is 100% true, but most textbooks do give the problem this way. However it makes no sense having the '+ 1' as the limits of integration are assumed to be there (for the 1st two integrals) but are needed for this last integral.

 

[pka]

Hi all. So I'm tutoring a student on another forum and I've found a problem that's given me some grief. I think there might be an error in the problem somewhere, and I just want to make sure I'm not going crazy or missing something obvious. The full text of the problem is:

Sorry to tell you but this is a non problem.
Unless there are limits of integration there can be no numerical value assigned to an indefinite integral.
Now it may be that who ever reposted may have been too lazy to use definite integral notation.
But without that the question is meaningless.
But if the question was posted correctly then the author does not understand integration theory.
Please review and repost.

 

[ksdhart2]

Sorry to tell you but this is a non problem.
Unless there are limits of integration there can be no numerical value assigned to an indefinite integral.
Now it may be that who ever reposted may have been too lazy to use definite integral notation.
But without that the question is meaningless.
But if the question was posted correctly then the author does not understand integration theory.
Please review and repost.

Well, at least it's not just me missing something obvious. What I wrote was exactly as it appeared in the textbook. I saw a photograph of it and everything. In hindsight, it should have been a red flag that the indefinite integrals were assigned numerical values, but I just kinda shut my brain off and ran with it. In any case, thanks for the confirmation.