Antiderivative of 0 Antiderivative of 0 Our question is to find the antiderivative of 0 ? So for calculating the antiderivative we have to know definition of antiderivative : in calculus, antiderivative is an operation which calculate opposite of derivatives means antiderivative calculate integration operation on derivative, like g(x) is a derivative of f(x), then we calculate antiderivative of g(x) by integration method and it produces f(x) as a result -d (f(x)) = g(x) then antiderivative of g(x) means integration of g(x) is âˆŤg(x) dx = f(x) + c dx
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For proving that antiderivative is an opposite operation of derivation, we take some examples like we have a function f(t) = t step 1 : Firstly we calculate derivative of f(t) is d (t) = 1.t1-0 = 1 dt step 2 : As we all know that antiderivative operation is behaving like integration operation, then if integration of 1 is produces original function than we can say that antiderivative operation is opposite operation of derivation . So, let’s check it - âˆŤ1 dx = t0+1 + c = t + c 0+1 it produces t as a result , which is our original function f(t). So, we can say that antiderivative is an opposite operation of derivation. So, we can say that if somebody knows derivation very well, than it’s very easy for them to calculate antiderivation operation on certain functions. Now, we discuss antiderivative of 0: As we all know that 0 is a derivative of constant (k) meansd (c) = 0 where c = 1,2,..........any constant number which includes all rational, irrational numbers
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dx then antiderivative of 0 is constant(k) because antiderivative is opposite operation of derivation : âˆŤ0 dx = 0 + c = c Here c is a constant . So, we can say that constant(c) is an antiderivative of 0.
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