Antiderivative of 0?

Question

What is the antiderivative of 0?

Answer 1

It's 0 + C. So it's just C.

Answer 2

We're being asked to integrate sin^3(-3x) and I think you need the condition on F to be evaluated at a number, not x, otherwise it doesn't make sense. (e.g. F(0) = 0). First, let u = -3x so du/dx = -3 and the integral becomes -1/3 int sin^3(u) du = -1/3 int sin^2(u)sin(u) du = -1/3 int [1 - cos^2(u)] sin(u)du. Now let w = cos(u) so dw/du = -sin(u) and the integral becomes 1/3 int [1 - w^2] dw = 1/3[w - w^3/3] + c = 1/3[cos(u) - 1/3cos^3(u)] + c = 1/3cos(-3x) [1 - 1/3cos^2(-3x)] + c. This is the antiderivative F(x) and if we apply the condition F(0) = 0, then we have 1/3[1 - 1/3(1)] + c = 0 or c = -2/9. Work out c using same procedure if F(0) = any other number.

Answer 3

That's 0 + C = C,
C a constant.

Answer 4

There is no anti-derivative to 0. Zero is nothing, if you are getting 0 as part of the equation, you add nothing to the rest of the equation.

Answer 5

any constant has a derivative of 0.
"the" antiderivative is misleading, implying there is only one.
The answer is "C", an arbitrary constant.

Answer 6

any constant because a derivative of a constant is always zero

Answer 7

integral of (0dx) = c, any constant.

because derivative of c is zero.