What is the integral of zero -- a constant or zero?

Question

That is, an arbitrary constant or zero?

Answer 1

Zero, simple. Although derivative of a constant would be zero, but integral of zero would always be zero. One thing to note: Integral is NOT antiderivative in strict sense. Its an area under graph f(x) in cartesian system, where it is ofcourse in a two dimensional plane.

Answer 2

Integral Of Zero

Answer 3

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RE:
What is the integral of zero -- a constant or zero?

Answer 4

It depends on the type of integral you're asking about.

As an indefinite integral (int(0,dx)), it is C. This is justified by stating that since there is no range involved, the derivative of a constant = 0, therefore the strict anti-derivative of 0 is any constant.

As a definite integral however (int(0,dx,a,b)), it is 0. This is justified by stating that the integral of any function is the area between its curve and the argument's axis over a range (ex. For f(x)=0, the area between f(x) as x goes from a to b and f(x)=0 is F(b)-F(a) which is 0(b)-0(a)=0)

Answer 5

You know that, integration is the reverse process of differentiation and then the differentiation of any constant number C is zero. if so integration of zero is any constant number C

Answer 6

Integrals are looking for the area under the graph. There is no area under the graph of y=0

If you take a derivative of of a horizontal line it'll be 0. Take a derivative of a diagonal line is a constant.

Answer 7

Hey there!

It can be 0, since the derivative of 0 is 0.

However it can be 1, since the derivative of 1 is 0.

It can be any arbitary constant, commonly referred to as C.

The derivative of C is 0, so vice versa, the integral of 0 is C.

Hope it helps!

Answer 8

Zero. Zero is a constant.

Answer 9

It's an arbitrary constant C, because the derivative
of C is 0.