What is the integral of 0? I am trying to convince

oliviayychengwh

oliviayychengwh

Answered question

2021-12-21

What is the integral of 0?
I am trying to convince my friend that the integral of 0 is C, where C is an arbitrary constant. He can't seem to grasp this concept. Can you guys help me out here? He keeps saying it is 0.

Answer & Explanation

esfloravaou

esfloravaou

Beginner2021-12-22Added 43 answers

Taking the derivative of any constant function is 0, i.e. ddxc=0. So the indefinite integral  0 dx produces the class of constant functions, that is f(x)=c for some c.
Theres
maul124uk

maul124uk

Beginner2021-12-23Added 35 answers

You are correct,  0 dx=0+C=C
Your friend is not entirely wrong because C could equal 0. ie. if f(x)=0 is one antiderivative. But in general we do not know C unless we are given some initial condition.
nick1337

nick1337

Expert2021-12-28Added 777 answers

Indefinite integrals (anti-derivatoves) are known modulo a constant function. With definite integrals, the case is different:
ab0dt=0
One way to verify that C is the anti-derivative of 0 is simply
ddtC=0

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