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. $