Question

Evaluate integrate |x - 2| dx from 0 to 4

Answer 1

Given:

`\int_0^4|x-2|dx`

Split the integral;

`\begin{gathered} \int_0^4|x-2|dx=\int_0^2-(x-2)dx+\int_2^4(x-2)dx \\ ==\int_0^2(-x+2)dx+\int_2^4(x-2)dx \end{gathered}`

Integrating the expression;

`\begin{gathered} =(-(x^2)/(2)+2x)|^2_0+((x^2)/(2)-2x)|^4_2 \\ Introducing\text{ the limits;} \\ =[(-(2^2)/(2)+2(2))-0]+[((4^2)/(2)-2(4))-((2^2)/(2)-2(2))] \\ =(-2+4)-(0)+(8-8)-(2-4) \\ =2+0+0-(-2) \\ =2+2 \\ =4 \end{gathered}`

Therefore, the answer is 4.

OPTION D is correct.