# Homework Help: Integrate dy/dx=0 and arbitrary constant?

1. Apr 17, 2012

### sharks

The problem statement, all variables and given/known data
Integrate:
$$\frac{dy}{dx}=0$$

The attempt at a solution
$$\int \frac{dy}{dx}=\int 0\,.dx$$
The answer is: $y=0$ or $y=0+A$?
This is the part which is confusing, as i know that integral of 0 is 0, but do i have to add a constant of integration??

2. Apr 17, 2012

### dikmikkel

How about a dy/dx which is as positive as negative over the interval, that could be zero. fix it was e.g. sin(x)
But yeah, a constant.

3. Apr 17, 2012

### sharks

Now that i think about it, here is a simple example:
Let $y=5$
$$\frac{dy}{dx}=0$$
Now, if i integrate 0, then i should normally get 5. So, the constant of integration has to be involved.

4. Apr 17, 2012

### Staff: Mentor

The above should be
$$\int \frac{dy}{dx}~dx=\int 0\,.dx$$
You are integrating both sides of the original equation, with respect to x.

Zero is merely one antiderivative of 0.

A simpler approach is as follows.
Since dy/dx = 0, then y must be a constant. IOW y $\equiv$ C.

Also, when you integrate both sides of an equation, there is a constant of integration for each side. So the integration that you did would look like this:
y + C1 = 0 + C2

Of course, you can subtract C1 from both sides to end up with y = C, where C = C2 - C1.

5. Apr 19, 2012

### sharks

Thank you for the clarification, Mark44.

6. Apr 19, 2012

### HallsofIvy

Most teachers will mark off on homework or a test if you do not include the "constant of integration". If F(x) is an anti- derivative of f(x)- that is, if F'(x)= f(x), then [itex]\int f(x)dx= F(x)+ C where C can be any number.