Find the value of _ ,0 ^ ,9 [ x + 2]dx , where [.] is the greates… - Vidyadip

MCQ

Find the value of $\int_{\,0}^{\,9} {[\sqrt x + 2]dx} ,$ where $[.]$ is the greatest integer function

✓
$31$
B
$22$
C
$23$
D
None of these

✓

Answer

Correct option: A.

$31$

a
(a) $\int_{\,0}^{\,9} {[\sqrt x + 2]} \,dx$

$ = \int_0^1 {2\,dx + \int_1^4 {3\,dx + \int_4^9 {4\,dx} } } $

$ = 2 + (12 - 3) + (36 - 16)$

$ = 2 + 9 + 20 = 31$.

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