Absolute value definite integral

[Mdhiggenz]

Homework Statement

∫[|2x-1|] evaluated on the interval [1,-1]

Homework Equations

The Attempt at a Solution

I know we must split it into two equations ∫ from [a,c] + ∫ from [c,b]

and in absolute value one is negative and one is positive, so it will be

2x-1, and 1-2x my question is how do we know which interval to place each one in.

Do we place 1-2x in the interval from [c,b] or 2x-1, and vice versa,

thank you

 

[SammyS]

Homework Statement

∫[|2x-1|] evaluated on the interval [1,-1]

Homework Equations

The Attempt at a Solution

I know we must split it into two equations ∫ from [a,c] + ∫ from [c,b]

and in absolute value one is negative and one is positive, so it will be

2x-1, and 1-2x my question is how do we know which interval to place each one in.

Do we place 1-2x in the interval from [c,b] or 2x-1, and vice versa,

thank you

Where is 2x-1 ≥ 0 ?

Where is 1-2x ≥ 0 ?

 

[Mdhiggenz]

for 2x-1 when x is greater than or = to 1/2

and for 1-2x when x is less than or = to 1/2

?

 

[SammyS]

for 2x-1 when x is greater than or = to 1/2

and for 1-2x when x is less than or = to 1/2

?

That should allow you to evaluate $\displaystyle \int_{-1}^1\ |2x-1|\,dx\,.$

 

[Mdhiggenz]

Ohh so what you are saying is since 1-2x is less than 1/2 it goes in the interval from [0,1/2]?