Question

Evaluate the following integral: `int_0^1|2x-1|d` x
A. `2`
B. `(1)/(2)`
C. `1`
D. `0`

Answer 1

Put `2x-1=t` and `dx=(1)/(2)dt`.
`[x=0impliest=-1]` and `[x=1impliest=1]`
`:.I=(1)/(2)int_(-1)^(1)|t|dt=(1)/(2){int_(-1)^(0)-tdt+int_(0)^(1)t}`
`=(1)/(2){[(-t^(2))/(2)]_(-1)^(0)+[(t^(2))/(2)]_(0)^(1)}=(1)/(2){(0+(1)/(2))+((1)/(2)-0)}=(1)/(2)`.