Definite Integration Question 82

Question: $ \int _{0}^{2}{|x-1|dx=} $

[SCRA 1990; RPET 2001; UPSEAT 2003]

Options:

A) 0

B) 2

C) 1/2

D) 1

Show Answer

Answer:

Correct Answer: D

Solution:

$ I=\int_0^{2}{|x-1|dx=\int_0^{1}{(-x+1)dx+\int_1^{2}{(x-1)dx}}} $

$ =( \frac{-x^{2}}{2}+x )_0^{1}+( \frac{x^{2}}{2}-x )_1^{2}=1. $