Definite Integration Question 287
Question: The area of the region bounded by the curves $ y=|x-2|, $
$ x=1,x=3 $ and the x-axis is
[AIEEE 2004]
Options:
A) 4
B) 2
C) 3
D) 1
Show Answer
Answer:
Correct Answer: D
Solution:
Required area $ =\int_1^{3}{|x-2|dx}=\int_1^{2}{(2-x)dx+\int_2^{3}{(x-2)dx}} $
$ =[ 2x-\frac{x^{2}}{2} ]_1^{2}+[ \frac{x^{2}}{2}-2x ]_2^{3} $
$ =\frac{1}{2}+\frac{1}{2}=1 $ .
BETA
