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
$\int_{ - \pi /2}^{\pi /2} {{{\sin }^2}x\,dx = } $
  • A
    $\pi $
  • ✓
    $\frac{\pi }{2}$
  • C
    $\frac{\pi }{2} - \frac{1}{2}$
  • D
    $\pi - 1$
✓

Answer

Correct option: B.
$\frac{\pi }{2}$
b
(b)$\int_{ - \pi /2}^{\pi /2} {{{\sin }^2}x\,dx = 2\int_0^{\pi /2} {{{\sin }^2}x\,dx = 2\frac{{\Gamma \left( {\frac{3}{2}} \right).\Gamma \left( {\frac{1}{2}} \right)}}{{2\Gamma \left( {\frac{{2 + 2}}{2}} \right)}}} = \frac{\pi }{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

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

Similar questions

For linear programming $x+2 y \geq 10,3 x+4 y \leq 24$ and $x \geq 0, y \geq 0 \ldots \ldots \ldots .$ is not the corner point of feasible region.
→
Let the angle $\theta, 0<\theta<\frac{\pi}{2}$ between two unit vectors $\hat{a}$ and $\hat{b}$ be $\sin ^{-1}\left(\frac{\sqrt{65}}{9}\right)$. If the vector $\vec{c}=3 \hat{a}+6 \hat{b}+9(\hat{a} \times \hat{b}), \quad$ then the value of $9(\vec{c} \cdot \hat{a})-3(\vec{c} \cdot \hat{b})$ is
→
One card is drawn randomly from a pack of $52$ cards, then the probability that it is a king or spade is
→
Which one of the following functions is not continuous on $(0,\pi )?$
→
All face cards from pack of $52$ playing cards are removed. From remaining $40$ cards two are drawn randomly without replacement, then probability of drawing a pair (same denominations) is 
→
If ${A_i} = \left[ {\begin{array}{*{20}{c}}{{a^i}}&{{b^i}}\\{{b^i}}&{{a^i}}\end{array}} \right]$and if $|a|\, < 1,\,|b|\, < 1$, then $\sum\limits_{i = 1}^\infty {\det ({A_i})} $is equal to
→
Let $a , ar , ar ^2,...........$ be an infinite $G.P.$ If $\sum_{n-0}^{\infty} a r^n=57$ and $\sum_{n-0}^{\infty} a^3 r^{3 n}=9747$, then $a+18 r$ is equal to $:$
→
Let $a$ be the sum of all coefficients in the expansion of $\left(1-2 x+2 x^2\right)^{2023}\left(3-4 x^2+2 x^3\right)^{2024}$ and $b=\lim _{x \rightarrow 0}\left(\frac{\int_0^x \frac{\log (1+t)}{t^{2024}+1} d t}{x^2}\right)$. If the equations $\mathrm{cx}^2+\mathrm{dx}+\mathrm{e}=0$ and $2 \mathrm{bx}^2+\mathrm{ax}+4=0$ have a common root, where $c, d, e \in R$, then $d: c: e$ equals
→
The volume of a spherical balloon is increasing at the rate of  $40$  cubic centrimetre per minute. The rate of change of the surface of the balloon at the instant when its radius is $8$  centimetre, is ........ $sq \,cm/\min$.
→
$\int_0^a {{x^2}\sin {x^3}\,dx} $ equals
→