# Simple Integral "Find what's wrong" question

#### tesstess

##### New member

Question in attached picture.
Thanks for the help, kinda forgot the simple rules of splitting integrals.
All that came to mind was no dx attached to each new integral.

Also side question: if the prompt says "Evaluate the integral using a substitution prior to integration by parts." how do I approach that, especially since the tabular method is easily applicable to the derivative.

Appreciate it <3333333

#### tkhunny

##### Moderator
Staff member
View attachment 10613
Question in attached picture.
Thanks for the help, kinda forgot the simple rules of splitting integrals.
All that came to mind was no dx attached to each new integral.

Also side question: if the prompt says "Evaluate the integral using a substitution prior to integration by parts." how do I approach that, especially since the tabular method is easily applicable to the derivative.

Appreciate it <3333333
"dx" is superfluous, anyway, so long as the context is clear.

Why do you suppose there is anything "wrong" with it? Really, though, just check the parentheses.

#### Jomo

##### Elite Member
View attachment 10613
Question in attached picture.
Thanks for the help, kinda forgot the simple rules of splitting integrals.
All that came to mind was no dx attached to each new integral.

Also side question: if the prompt says "Evaluate the integral using a substitution prior to integration by parts." how do I approach that, especially since the tabular method is easily applicable to the derivative.

Appreciate it <3333333
$$\displaystyle \int$$(f(x)+/-g(x))dx = $$\displaystyle \int$$f(x)dx +/- $$\displaystyle \int$$g(x)dx and $$\displaystyle \int$$kf(x)dx = k$$\displaystyle \int$$f(x)dx, for some constant k.
You need these two to do problems like your. One problem is that there are no dx's but there is another problem.

Last edited:

#### pka

##### Elite Member
View attachment 10613
Question in attached picture.
Thanks for the help, kinda forgot the simple rules of splitting integrals.
All that came to mind was no dx attached to each new integral.
I agree with tkh that $$\displaystyle dx$$ is totally irrelevant.
This is a poor question, it is a bad 'grouping' question.
$$\displaystyle \int {\left[ {fg + 4h - g} \right]} = \int {fg} + 4\int h - \int g$$

#### tesstess

##### New member
"dx" is superfluous, anyway, so long as the context is clear.

Why do you suppose there is anything "wrong" with it? Really, though, just check the parentheses.
The homework question prompt asked for whats wrong with it.
So I'm assuming through your response technically there should be "dx"'s and I need to comment on the solution's use of parentheses?

Thanks for the response! <3

#### Harry_the_cat

##### Full Member
View attachment 10613
Question in attached picture.
Thanks for the help, kinda forgot the simple rules of splitting integrals.
All that came to mind was no dx attached to each new integral.

Also side question: if the prompt says "Evaluate the integral using a substitution prior to integration by parts." how do I approach that, especially since the tabular method is easily applicable to the derivative.

Appreciate it <3333333
The statement will be correct if the square brackets on the RHS are removed.

#### Dr.Peterson

##### Elite Member
I think it should be mentioned that the dx is not entirely irrelevant; many teachers will insist on it, though it is not nearly as important as the parenthesization in this example. So it may well be expected in the answer to this question.

It has several purposes, varying according to context:
• merely identifying the variable with respect to which you are integrating;
• (often) marking the end of the integrand;
• making the connection to definite integrals as sums (in fact, sums (∫ = S) of small differences (d));
• clarifying the fact that, as an antiderivative, the integral operates on (and undoes) a differential, so that ∫du = u;
• making the dimensional analysis work out.
It becomes much more important in multiple integrals, and is not needed when you just write ∫f as opposed to ∫f(x); but teachers who insist on it do have good reason to do so.

#### tkhunny

##### Moderator
Staff member
The statement will be correct if the square brackets on the RHS are removed.
Fair enough, the dx is not TOTALLY irrelevant, but

There is NO difference: $$\displaystyle \int\;f(x)\;dx = \int\;dx\;f(x) = \int\;f(x)$$

The context must be CLEAR.

Textbook convention and/or teacher requirements my disagree.