What is the antiderivative of #2x#?

Answer 1

There are many antiderivatives of #2x#. The (most) general antiderivative is #x^2 +C#

An antiderivative of #2x# is a function whose derivative is #2x#:

antiderivatives include:

#x^2#, #" "x^2+7#, #" "x^2+19#, #" "x^2-11#, #" "x^2+(17pi)/8 - sqrt 21#
#x^2 +sin^2x+cos^2x#
Any (every) function that can be expressed in the form #x^2 + "some constant"# is an antiderivative.
The general antiderivative is expressed by choosing one of the antiderivatives and adding an "arbitrary constant" usually named #C#

It is convenient (but not required) to choose the first antiderivative on the list above and say:

The (most) general antiderivative of #2x# is #x^2 + C#.
Strange but true According to the definition of general antiderivative, we can also say "The (most) general antiderivative of #2x# is #x^2+sin^2x+cos^2x+19sqrtpi - sqrt37/4 +C#"

Important! -- check you textbook's definition (and your grader's sense of humor) before using this smart-alecky answer on an exam!

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Answer 2

The antiderivative of 2x is x^2 + C, where C is the constant of integration.

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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.

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.

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.

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.

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