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What is the antiderivative of zero?
The antiderivative of a function which is equal to 0 everywhere is a function equal to 0 everywhere.
Can anyone of can prove that antiderivative is wrong?
The way to disprove an antiderivative is to simply differentiate the function and see if it matches the integral expression. Remember that an antiderivative expression must include a term often coined "C-" an arbitrary constant. For example, ∫(x^3 +14x)dx= (1/4)X^4+ 7X^2 +C. To verify that this is correct, take the derivative. You get x^3 +14x.
Can a function have more than one antiderivative?
yes, look at the function f(x)=3x^2 The antiderivative is x^3+C where C is the constant and is more than one value for C. In fact, 3x^2 will have an infinite number of antiderivatives.
What is the fundamental theory of calculus?
The fundamental theorum of calculus states that a definite integral from a to b is equivalent to the antiderivative's expression of b minus the antiderivative expression of a.
What is the antiderivative of e to the -x?
-e-x + C.
