Download App

STD 12 - 7.2 definite integral — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 7.2 definite integral4 Marks
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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let the line L pass through $(1,1,1)$ and intersect the lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-4}{2}=\frac{z}{1}$ . Then, which of the following points lies on the line L?
→
Let $\left\{a_{n}\right\}_{n=0}^{\infty}$ be a sequence such that $a _{0}= a _{1}=0$ and $a _{ n +2}=2 a _{ n +1}- a _{ n }+1$ for all $n \geq 0$. Then, $\sum\limits_{ n =2}^{\infty} \frac{ a _{ n }}{7^{ n }}$ is equal to
→
Let the mean and variance of the frequency distribution

$\mathrm{x}$ $\mathrm{x}_{1}=2$ $\mathrm{x}_{2}=6$ $\mathrm{x}_{3}=8$ $\mathrm{x}_{4}=9$
$\mathrm{f}$ $4$ $4$ $\alpha$ $\beta$

be $6$ and $6.8$ respectively. If $x_{3}$ is changed from $8$ to $7 ,$ then the mean for the new data will be:

→
An $n$-digit number is a positive number with exactly $n$ digits. Nine hundred distinct $n$-digit numbers are to be formed using only the three digits $2, 5$ and $7$. The smallest value of $n$ for which this is possible is
→
The complex number $z = x + iy$ which satisfy the equation $\left| {\frac{{z - 5i}}{{z + 5i}}} \right| = 1$ lie on
→
$\left( {\frac{{\sin 2A}}{{1 + \cos 2A}}} \right)\,\left( {\frac{{\cos A}}{{1 + \cos A}}} \right)= $
→
How many different words can be formed by jumbling the letters in the word $MISSISSIPPI$ in which no two $S$ are adjacent $?$
→
$6$ Boys and $5$ girls sit in a line so that $(I)$ no two girls sit together $(II)$ all the girls sit together. If $p$ is the number of arrangements in case $(I)$ and $q$  in case $(II)$ then $p/q =$
→
The number of the real roots of the equation $(x+1)^{2}+|x-5|=\frac{27}{4}$ is ....... .
→
The value of $\left(\sin 70^{\circ}\right)\left(\cot 10^{\circ} \cot 70^{\circ}-1\right)$ is
→