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What is the definite integral of 0?

Answer 1

Emily Ammerman

There's no single answer if there were to be no boundaries. Since there are boundaries:

#d/(dx)[C] = 0# where #C# is any constant.

#int_a^b f(x)dx# can be taken as #sum_(x_i=a)^(b) f(x_i) Deltax_i#, so with #f(x) = 0#:

#sum_(x_i=a)^(b) 0 Deltax_i = 0sum_(x_i=a)^(b) Deltax_i = 0#

Or, you could say that #f(x) = 0#, thus it has no area between itself and the x-axis when restricted to a boundary.

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Answer 2

Isabella Ackerman

The definite integral of the constant function 0 over any interval is always 0.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.