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$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 7.2 definite integral→7.2 definite integral — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

What is the maximum value of function $f(x)=\sin x+\cos x$ ?

Consider the following events :

$E_1$ : Six fair dice are rolled and at least one die shows six.

$E_2$ : Twelve fair dice are rolled and at least two dice show six.

Let $p_1$ be the probability of $E_1$ and $p_2$ be the probability of $E_2$. Which of the following is true?

$\int_{}^{} {\frac{{dx}}{{(1 + {x^2})\sqrt {{p^2} + {q^2}{{({{\tan }^{ - 1}}x)}^2}} }}} = $

Choose the correct answer from the given four options.
The probability that exactly two of the three balls were red, the first ball being red, is:

Let $R$ be the relation on the set of all real numbers defined by $a R b$ iff $|a-b| \leq 1$. Then, $R$ is

The direction cosines l, m, n of two lines are connected by the relations l + m + n = 0, lm = 0, then the angle between them is:

$\frac{\pi}{3}$
$\frac{\pi}{4}$
$\frac{\pi}{2}$
$0$

If $\text{y}=2\sin\text{x}+\sin2\text{x}$ for $0≤\text{x}≤2\pi,$ then the area enclosed by the curve and x-axis is:

$\frac{9}{2}\text{sq.}\text{units}$
8 sq. units
12 sq. units
4 sq. units

If $x = a(t + \sin t)$ and $y = a(1 - \cos t)$, then ${{dy} \over {dx}}$ equals

Consider a quadratic equation $ax^2 + bx + c = 0,$ where $2a + 3b + 6c = 0$ and let $g(x) = a\frac{{{x^3}}}{3} + b\frac{{{x^2}}}{2} + cx.$

Statement $1:$ The quadratic equation has at least one root in the interval $(0, 1).$

Statement $2:$ The Rolle's theorem is applicable to function $g(x)$ on the interval $[0, 1 ].$

The inverse of the matrix $\left[ {\begin{array}{*{20}{c}}1&0&0\\0&1&0\\0&0&1\end{array}} \right]$ is