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Definite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
The value of $\int_0^9[\sqrt{x}+2] d x$, where [.] is the greatest integer function, is
  • ✓
    31
  • B
    22
  • C
    23
  • D
    None of these
✓

Answer

Correct option: A.
31
(A)
$\int_0^9[\sqrt{x}+2] d x$
$\begin{array}{l}=\int_0^1[\sqrt{x}+2] d x+\int_1^4[\sqrt{x}+2] d x+\int_4^9[\sqrt{x}+2] d x \\ =\int_0^1 2 d x+\int_1^4 3 d x+\int_4^9 4 d x \\ =2+3(4-1)+4(9-4)=2+9+20=31\end{array}$

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