Definite Integration Question 17
Question: If $
[x] $ denotes the greatest integer less than or equal to $ x, $ then the value of the integral $ \int_0^{2}{x^{2}[x]dx} $ equals [Kurukshetra CEE 1996; Pb. CET 2001]
Options:
A) 5/3
B) 7/3
C) 8/3
D) 4/3
Show Answer
Answer:
Correct Answer: B
Solution:
$ \int_0^{2}{x^{2}[x]dx=\int_0^{1}{x^{2}(0)dx+\int_1^{2}{x^{2}(1)dx=0+[ \frac{x^{3}}{3} ]}_1^{2}=\frac{7}{3}}} $ .
BETA
