Find the Anti-Derivative |x|

Math
Write as a function.
The function can be found by finding the indefinite integral of the derivative .
Set up the integral to solve.
Set the argument in the absolute value equal to to find the potential values to split the solution at.
Simplify the answer.
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Create intervals around the solutions to find where is positive and negative.
Substitute a value from each interval into to figure out where the expression is positive or negative.
Integrate the argument of the absolute value.
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Set up the integral with the argument of the absolute value.
By the Power Rule, the integral of with respect to is .
On the intervals where the argument is negative, multiply the solution of the integral by .
Combine and .
Simplify.
Simplify.
The answer is the antiderivative of the function .
Find the Anti-Derivative |x|

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