Download App

7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
$\int\limits_{ - 2}^\pi  {\frac{{{{\sin }^2}x}}{{\left[ {\frac{x}{\pi }} \right] + \frac{1}{2}}}} \,dx$ is equal to               (where $[·]$ denotes the greatest integer function)
  • A
    $\pi  + \sin 2\cos 2$
  • ✓
    $\pi  - 2 + \sin 2\cos 2$
  • C
    $\pi  - 2 - \sin 2\cos 2$
  • D
    None
✓

Answer

Correct option: B.
$\pi  - 2 + \sin 2\cos 2$
b
$\int_{-2}^{0} \frac{\sin ^{2} x}{-1+\frac{1}{2}} d x+\int_{0}^{\pi} \frac{\sin ^{2} x}{0+\frac{1}{2}} d x$

$-\int_{-2}^{0} 2 \sin ^{2} x d x+\int_{0}^{\pi} 2 \sin ^{2} x d x$

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

Consider  $f (x) = | 1 - x | \,;\,1 \le x \le 2 $   and $g (x) = f (x) + b sin\,\frac{\pi }{2}\,x$, $1 \le x \le 2$  then which of the following is correct ?
→
$\int {\frac{{dx}}{{\sin (x - a)\sin (x - b)}}} $ is
→
If $a \times (b \times c) = 0,$ then
→
Let $\alpha \in(0, \infty)$ and $A=\left[\begin{array}{lll}1 & 2 & \alpha \\ 1 & 0 & 1 \\ 0 & 1 & 2\end{array}\right]$. If $\operatorname{det}\left(\operatorname{adj}\left(2 \mathrm{~A}-\mathrm{A}^{\mathrm{T}}\right) \cdot \operatorname{adj}\left(\mathrm{A}-2 \mathrm{~A}^{\mathrm{T}}\right)\right)=2^8$, then $(\operatorname{det}(\mathrm{A}))^2$ is equal to :
→
The angle between the vectors $i - j + k$ and $i + 2j + k$ is
→
The value of $\int_{\, - 2}^{\,2} {\left[ {p\ln \left( {\frac{{1 + x}}{{1 - x}}} \right) + q\ln {{\left( {\frac{{1 - x}}{{1 + x}}} \right)}^{ - 2}} + r} \right]\,dx} $ depends on
→
If $f (\alpha)=\int_{1}^{\alpha} \frac{\log _{10} t}{1+t} d t, \alpha>0$, then $f \left( e ^{3}\right)+ f \left( e ^{-3}\right)$ is equal to.
→
Let $I$ be the purchase value of an equipment and $V(t)$ be the value after it has been used for $ t $ years. The value $V(t)$ depreciates at a rate given by differential equation $\frac{{dV\left( t \right)}}{{dt}} = - k\left( {T - t} \right)$ where $k > 0$ is a constant and $T$ is the total life in years of the equipement. Then the scrap value  $V(T)$ of the equipment is 
→
If ${\Delta _1} = \left| {\begin{array}{*{20}{c}}
  x&{\sin \,\theta }&{\cos \,\theta } \\ 
  {\sin \,\theta }&{ - x}&1 \\ 
  {\cos \,\theta }&1&x 
\end{array}} \right|$ and ${\Delta _1} = \left| {\begin{array}{*{20}{c}}
  x&{\sin \,2\theta }&{\cos \,\,2\theta } \\ 
  {\sin \,2\theta }&{ - x}&1 \\ 
  {\cos \,\,2\theta }&1&x 
\end{array}} \right|$, $x \ne 0$ ; then for all $\theta  \in \left( {0,\frac{\pi }{2}} \right)$
→
If $u = {\sin ^{ - 1}}\left( {{y \over x}} \right),$ then ${{\partial u} \over {\partial x}}$ is equal to
→