Definite Integration Question 65
Question: Find the value of $ \int _{0}^{9}{[\sqrt{x}+2]dx}, $ where [.] is the greatest integer function
[UPSEAT 2002]
Options:
A) 31
B) 22
C) 23
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ \int _{0}^{9}{[\sqrt{x}+2]}dx $
$ =\int_0^{1}{2dx+\int_1^{4}{3dx+\int_4^{9}{4dx}}} $
$ =2+(12-3)+(36-16) $
$ =2+9+20=31 $ .
BETA
