How to solve an absolute value integral?

[physicsernaw]

Homework Statement

∫0-->x |t|dt

Homework Equations

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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|).

 

[tiny-tim]

hi physicsernaw!

(try using the X² button just above the Reply box )

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

how did you get that?

it should be -1/2 x² ​