afruff23

What is the indefinite integral of 0?

What is the anti-derivative of 0?

Is there a difference?

TarHeel3007

i think its 0. area under y=0 is 0...
anti derivative = integral too right?

thorps517

integral of 0 is just C .... so it could be any number

indefinite integral and anti deriv are the same = some C
but the definite integral, is always just 0

correct me if im wrong anybody

dylalien

There is no indefinite integral of zero! And even if there were, it sure as hell wouldn't be C. Any number times zero is zero!

Lemme spell it out for you. The integral of a constant is that constant times the length of the interval... We can all picture the rectangle, can we not? Now, if the constant is zero, it doesn't matter what the length of the interval is, as the area will always be zero.

afruff23

"There is no indefinite integral of zero! And even if there were, it sure as hell wouldn't be C. Any number times zero is zero!"

So the answer is zero not "There is no indefinite integral of zero".

TheMathProf

I actually think the correct answer is C.

Only the definite integral is approximated using area.

The antiderivative, or the indefinite integral, represents a function whose derivative gives you 0. Any constant does this.

Think about it: the derivative of 5 is 0. The derivative of 17 is 0. The derivative of -2/3 is 0.

So when you're asked, what is the antiderivative of 0? You have to say, it's some constant.

Now the definite integral, on any interval [a, b], has to be 0, for the reasons mentioned by dylalien.

applesauce

^^ Agreed with TheMathProf. I took calc last year and forgot, but his/her explanation jiggled my memory and it makes sense.