Definite Integration Question 227
Question: The area of the region bounded by $ y=|x-1| $ and $ y=1 $ is
[IIT Screening 1994]
Options:
A) 2
B) 1
C) $ \frac{1}{2} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ y=x-1, $ if $ x>1 $ and $ y=-(x-1), $ if $ x<1 $ Area $ =\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} ]+[ -( \frac{1}{2}-1 ) ] $
$ =\frac{1}{2}+\frac{1}{2}=1 $ .
BETA
