Definite Integration Question 91
Question: If $ f(x)=|x-1| $ , then $ \int_0^{2}{f(x)dx} $ is
[Orissa JEE 2004]
Options:
A) 1
B) 0
C) 2
D) -2
Show Answer
Answer:
Correct Answer: A
Solution:
Given $ f(x)=|x-1| $
$ \int_0^{2}{f(x)dx=\int_0^{2}{\text{ }|x-1|dx}}=\int_0^{1}{(1-x)dx+\int_1^{2}{(x-1)dx}} $
$ =[ x-\frac{x^{2}}{2} ]_0^{1}+[ \frac{x^{2}}{2}-x ]_1^{2} $
$ =( 1-\frac{1}{2} )+(2-2)-( \frac{1}{2}-1 )=1 $ .
BETA
