# I Notation help

1. Sep 20, 2016

### BillhB

Is there some standardized math text with "proper universal notation" I could read for calculus?

In one of my courses, $$\int\frac{dx}{x}$$ had a red mark through it, with a note that said "impossible" or something. I earned a zero on the question due to the above. In another instance $$\int(x^{-2}v)'dx$$ had a red-mark that said it was equal to zero and said terrible. In the same question $v'=yy'$ during a substitution had a mark that just said terrible. I got two points for the question, even though the answer matched others who had gotten full credit so I'm assuming I was just marked down for notation.

What's wrong with the above? Maybe this instructor just hates prime notation....

2. Sep 21, 2016

### Staff: Mentor

I would ask your instructor about it. It may not be notation but perhaps Something more fundamental.

In the first, your teacher may not have liked you dividing the $dx$ by $x$ and would have preferred that you wrote $(1/x) dx$ instead. It doesn't make sense to divide $dx$as it's not a value but a kind of placeholder that indicates what variable to integrate over.

In the second, I'd say the prime In the integral means that $f(x)' dx$ integrates to $f(x)$. If that not what you meant then you can see your teachers concern.

Last edited: Sep 21, 2016
3. Sep 21, 2016

### Staff: Mentor

What you show above is an indefinite integral. Was the integral that the instructor marked a definite integral?
Again, was the actual integral a definite integral?
What do v' and y' mean here? Prime notation doesn't show which variable the derivative is taken with respect to.

4. Sep 21, 2016

### Staff: Mentor

I don't think this is very likely. $\int \frac{dx}{x}$ is a wellknown integral that is often written this way.

5. Sep 21, 2016

### BillhB

No. It was just a simple separable differential equation.. $$\frac{dy}{dx}=\frac{1}{x}$$ $$\int{dy}=\int \frac{dx}{x}$$ $$y=ln|x| + C$$

It was just me writing out of a substitution for a Bernoulli Equation.. $$xy\frac{dy}{dx}+x^2-y^2=0$$ $$\frac{dy}{dx}-yx^{-1}=-xy^{-1}$$ so I had $v=y^2$, $v'=2yy'$ so I guess v' would be $\frac{dv}{dx}$ and y' is $\frac{dy}{dx}$ then I multiplied, found integrating factor, and subbed out to get to $$\int(vx^{-2})'dx=\int\frac{-2dx}{x}$$ $$vx^{-2}=-2ln|x|+C$$

Yeah, we've wrote it that way in earlier courses, no one seemed to mind. Physics professor always puts the differential in the expression... but she's a physics teacher, and probably doesn't care as much if it is wrong. The instructor was trying to show how it was wrong in the very next class, but I didn't really follow the "proof" that well.

Last edited: Sep 21, 2016
6. Sep 21, 2016

### Staff: Mentor

I don't see anything wrong with this, speaking as a former college math teacher of 18 years. I would ask the instructor why it was marked off.
You have a sign error in the 2nd equation.

7. Sep 21, 2016

### BillhB

Whoops, fixed it.

Okay, but he seemed adamant that it was "wrong" notation. Terrible, terrible notation, garbage notation notes give that kind of vibe. Just a bit worried, have an exam in that class soon. Most of my quiz scores are abysmal due to notation I guess. To be fair, some it's certainty because I made errors like the above, missing a sign..etc. The problems are long, so I'm working on being more careful. Was kind of hoping there was some kind of one stop shop for "proper notation."

8. Sep 21, 2016

### Staff: Mentor

What you have here -- $\int(vx^{-2})'dx=\int\frac{2dx}{x}$ isn't very good. An improvement would be $\int d(vx^{-2})=\int\frac{2dx}{x}$

If your instructor is dinging you for $\int \frac{dx} x$, s/he is being pedantic, IMO.

9. Sep 21, 2016

### BillhB

Got it.

Just worried about what other notation 'mistakes' I'm not aware of.

For your first question I believe he was looking for $\int \frac{dy}{dx}dx=\int \frac{dx}{x}$. Writing $\int dy$ should not be used, until you are taking a differential equations course.