How to solve an absolute value integral?

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The integral ∫0 to x |t| dt is evaluated as 1/2*x^2 for x >= 0 and 1/2*(-x)^2 for x <= 0. There is confusion regarding the negative sign for x <= 0, with some suggesting it should be -1/2*x^2. The book's answer is presented as 1/2*x|x|, which aligns with the piecewise evaluation of the absolute value function. The discussion highlights the importance of correctly handling the absolute value in integrals. Clarification on the evaluation process is sought among participants.
physicsernaw
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Homework Statement



∫0-->x |t|dt

Homework Equations



//

The Attempt at a Solution



1/2*x^2 for x>= 0

1/2*(-x)^2 for x<= 0

Not sure what to do to be honest. (the answer in the back of the book says 1/2*x|x|).
 
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hi physicsernaw! :smile:

(try using the X2 button just above the Reply box :wink:)
physicsernaw said:
1/2*(-x)^2 for x<= 0

how did you get that?

it should be -1/2 x2 :smile:​
 

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