_0^ 1.5 [ x^2 ] ,dx , where [ , ,. , ,] denotes the greatest inte… - Vidyadip

MCQ

$\int_0^{1.5} {[{x^2}]\,dx} $, where $[\,\,.\,\,]$ denotes the greatest integer function, equals

A
$2 + \sqrt 2 $
✓
$2 - \sqrt 2 $
C
$ - 2 + \sqrt 2 $
D
$ - 2 - \sqrt 2 $

✓

Answer

Correct option: B.

$2 - \sqrt 2 $

b
(b) $\int_0^{1.5} {[{x^2}]dx = \int_0^1 {[{x^2}]dx + \int_1^{\sqrt 2 } {[{x^2}]dx + \int_{\sqrt 2 }^{1.5} {[{x^2}]dx} } } } $

$ = 0 + \int_1^{\sqrt 2 } {1dx + \int_{\sqrt 2 }^{1.5} {2dx = \sqrt 2 - 1 + 3 - 2\sqrt 2 = 2 - \sqrt 2 } } $.

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 STD 12 - 7.2 definite integral→STD 12 - 7.2 definite integral — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Let $h(x) = \int\limits_0^x {g(t)dt}$ , where $g(x)$ is a differentiable and odd function $\forall x \in R$ and $g(x)$ is periodic with period $3$.

Statement $1 :$ $h(x) + h(-x) = 0$ $\forall x \in R$

Statement $2 :$ $h(x) + h(-x) = 2 \int\limits_0^x {g(t)dt} \forall x \in R$

Statement $3 :$ $h(3n) = 0 \forall n \in I$

then which of the following statement $(s)$ is $/$ are true ?

If $\vec{\text{a}}$ and $\vec{\text{b}}$ are unit vectors, then which of the following values of $\vec{\text{a}}.\vec{\text{b}}$ is not possible?

The differential equation of the family of curves, $x^{2}=4 b(y+b), b \in R,$ is

If $0 < x < 1$, then $\sqrt{1+x^2}\left[\left\{x \cos \left(\cot ^{-1} x\right)+\sin \left(\cot ^{-1} x\right)\right\}^2-1\right]^{1 / 2}$ is equal to

The roots of the equation $\left|\begin{array}{ccc}x & 0 & 8 \\ 4 & 1 & 3 \\ 2 & 0 & x\end{array}\right|$ = 0 are

The shortest distance between the $z-$ axis and the line $x + y + 2z - 3\, = 0 \,= 2x + 3y + 4z - 4$, is

If A and B are two events, then $\text{P}(\overline{\text{A}}\cap\text{B})=$

For all real values of $x$ , increasing function $f(x)$ is

If $y\sqrt {{x^2} + 1} = \log \left\{ {\sqrt {{x^2} + 1} - x} \right\}$, then $({x^2} + 1){{dy} \over {dx}} + xy + 1 = $

The area bounded by the curve $y=x^4-2 x^3+x^2+3$ with $x-$ axis and ordinates corresponding to the minima of $y$ is :