Definite Integration Question 134
Question: What is the area under the curve $ y=| x |+| x-1 | $ between $ x=0 $ and $ x=1 $ -
Options:
A) $ \frac{1}{2} $
B) 1
C) $ \frac{3}{2} $
D) 2
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ | x | $ for $ x\ge 0 $ = x and $ | x-1 | $ for $ x\le 1=-(x-1), $ So, $ \int_0^{1}{(| x |+| x-11 |)=} $ required area $ a=\int_0^{1}{xdx-\int_0^{1}{(x-1)dx}} $
$ =[ \frac{x^{2}}{2} ]_0^{1}-[ \frac{x^{2}}{2}-x ]_0^{1}=\frac{1}{2}-( \frac{1}{2}-1 )=1 $ sq. units
BETA
