Download App

STD 12 - 7.2 definite integral — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 7.2 definite integral1 Mark
MCQ
The value of $\int_\pi ^{2\pi } {[2\sin x]\,dx,} $ where $[\,\,.\,\,]$ represents the greatest integer function, is
  • A
    $ - \pi $
  • B
    $ - 2\pi $
  • ✓
    $ - \frac{{5\pi }}{3}$
  • D
    $\frac{{5\pi }}{3}$
✓

Answer

Correct option: C.
$ - \frac{{5\pi }}{3}$
c
(c) $\int_\pi ^{2\pi } {[2\sin x]dx = \int_\pi ^{\pi + (\pi /6)} {( - 1)dx + \int_{\pi + (\pi /6)}^{\pi + (\pi /2)} {\,( - 2)dx} } } $

$ + \int_{\pi + (\pi /2)}^{\pi + (\pi /2) + (\pi /3)} {\,( - 2)dx + \int_{\pi + (\pi /2) + (\pi /3)}^{2\pi } {\,( - 1)dx} } $

$ = - \frac{\pi }{6} - 2\left[ {\frac{\pi }{2} - \frac{\pi }{6}} \right] - 2\left[ {\frac{\pi }{3}} \right] - 1\left[ {\frac{\pi }{2} - \frac{\pi }{3}} \right]$

$ = - \frac{\pi }{6} - \frac{{2\pi }}{3} - \frac{{2\pi }}{3} - \frac{\pi }{6}$

$ = - \frac{\pi }{6} - \frac{{8\pi }}{6} - \frac{\pi }{6}$

$= - \frac{{10\pi }}{6} = - \frac{{5\pi }}{3}$.

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

$\text{A}^2=\text{I} \Rightarrow$
→
The number of solutions of $y' = \frac{{y + 1}}{{x - 1}},\,y(1) = 2$ is
→
If $ \frac{3\text{x}+1}{(\text{x}-1)(\text{x}+3)} = \frac{\text{A}}{\text{x}-1}+\frac{B}{\text{x}+3} $ then $ {\sin}^{-1} \frac{\text{A}}{\text{B}} :$
→
If the ratio of base radius and height of a cone is 1 : 2 and percentage error in radius is $\lambda\%,$ then the error in its volume is:
→
The solution of the differention equation $\frac{\text{dy}}{\text{dx}}=\frac{\text{x}^{2}+\text{xy}+\text{y}^{2}}{\text{x}^{2}}$ is:
→
Choose the correct answers from the given four options : The function $\text{f(x)}=\frac{4-\text{x}^2}{4\text{x}-\text{x}^3}$ is :
→
$A$ and $B$ are events such that $P(A)=0.4, P(B)$ $=0.3$ and $P(A \cup B)=0.5$. Then $P\left(B^{\prime} \cap A\right)$ equals
→
For the function $f(x) = \left\{ \begin{array}{l}\frac{{{{\sin }^2}ax}}{{{x^2}}},\,{\rm{when\,\,}}\,x \ne 0\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,1,{\rm{when\,\,}}\,x = 0\end{array} \right.$ which one is a true statement
→
$\int_{}^{} {{{\sec }^{2/3}}x\,{\rm{cose}}{{\rm{c}}^{4/3}}x\;dx = } $
→
Let $\ell_1$ and $\ell_2$ be the lines $\overrightarrow{\mathfrak{1}}_1=\lambda(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})$ and $\vec{r}_2=(\hat{\mathrm{j}}-\hat{\mathrm{k}})+\mu(\hat{\mathrm{i}}+\hat{\mathrm{k}})$, respectively. Let $\mathrm{X}$ be the set of all the planes $\mathrm{H}$ that contain the line $\ell_1$. For a plane $\mathrm{H}$, let $\mathrm{d}(\mathrm{H})$ denote the smallest possible distance between the points of $\ell_2$ and $H$. Let $\mathrm{H}_0$ be plane in $X$ for which $\mathrm{d}\left(\mathrm{H}_0\right)$ is the maximum value of $\mathrm{d}(\mathrm{H})$ as $\mathrm{H}$ varies over all planes in $\mathrm{X}$.

Match each entry in List-$I$ to the correct entries in List-$II$.

List-$I$  List-$II$ 
($P$) The value of $\mathrm{d}\left(\mathrm{H}_0\right)$ is ($1$) $\sqrt{3}$
($Q$) The distance of the point $(0,1,2)$ from $\mathrm{H}_0$ is ($2$) $\frac{1}{\sqrt{3}}$
($R$) The distance of origin from $\mathrm{H}_0$ is ($3$) $0$
($S$) The distance of origin from the point of intersection of planes $\mathrm{y}=\mathrm{z}, \mathrm{x}=1$ and $\mathrm{H}_0$ is ($4$) $\sqrt{2}$
  ($5$) $\frac{1}{\sqrt{2}}$

The corret option is :

→