Definite Integration Question 42
Question: If
[x] denotes the greatest integer less than or equal to x, then the value of $ \int _{1}^{5}{[|x-3|]dx} $ is [Roorkee 1999]
Options:
A) 1
B) 2
C) 4
D) 8
Show Answer
Answer:
Correct Answer: B
Solution:
$ I=\int_1^{5}{[|x-3|]}dx $
$ \Rightarrow I=\int_1^{3}{[-(x-3)]dx+\int_3^{5}{[ (x-3) ]}dx} $
$ \Rightarrow I=\int_1^{2}{[-(x-3)}]dx+\int_2^{3}{[-(x-3)]dx+}\int_3^{4}{[x-3]dx+\int_4^{5}{[x-3]dx}} $
$ \Rightarrow I=\int_1^{2}{dx}+\int_2^{3}{0dx+\int_3^{4}{0dx+\int_4^{5}{dx}}} $
$ =[x]_1^{2}+[x]_4^{5} $
$ \Rightarrow I=(2-1)+(5-4)=2 $ .
BETA
