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
$\mathop \smallint \limits_0^\pi \sqrt {1 + 4{{\sin }^2}\frac{x}{2} - 4\sin \frac{x}{2}} \;dx = $
  • A
    $4\sqrt 3 - 4$
  • ✓
    $\;4\sqrt 3 - 4 - \frac{\pi }{3}$
  • C
    $\pi - 4\;$
  • D
    $\frac{{2\pi }}{3} - 4\sqrt 3 - 4$
✓

Answer

Correct option: B.
$\;4\sqrt 3 - 4 - \frac{\pi }{3}$
b
$\int\limits_0^\pi  {\left| {\left( {1 - 2\sin \frac{x}{2}} \right)} \right|} dx$

$ = \int\limits_0^{\frac{\pi }{3}} {\left| {\left( {1 - 2\sin \frac{x}{2}} \right)} \right|} dx - \int\limits_{\frac{\pi }{3}}^\pi  {\left| {\left( {1 - 2\sin \frac{x}{2}} \right)} \right|} dx$

$=\left(x+4 \cos \frac{x}{2}\right)_{0}^{\frac{\pi}{3}}-\left(x+4 \cos \frac{x}{2}\right)_{\frac{\pi}{3}}^{\pi}$

$=\frac{\pi}{3}+4 \cos \frac{\pi}{6}-0-4-\left(\pi+4 \cos \frac{\pi}{2}-\frac{\pi}{3}-4 \cos \frac{\pi}{6}\right)$

$=-\frac{\pi}{3}+4 \sqrt{3}-4$

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

Choose the correct answer from the given four option. Integrating factor of $\frac{\text{xd}\text{y}}{\text{d}\text{x}}-\text{y}=\text{x}^4-3\text{x}$ is :
→
If the range of $f(x) = \frac{2x^2-14x^2-8x+49}{x^4-7x^2-4x+23}$ is ($a, b$], then ($a +b$) is
→
The solution of the differential equartion $y_1y_3 = y_2$ is :
→
Let $M$ and $N$ be two $3 \times 3$ non-singular skew-symmetric matrices such that $M N=N M$. If $P^T$ denotes the transpose of $P$, then $M^2 N^2\left(M^T N\right)^{-1}\left(M N^{-1}\right)^T$ is equal to

$(A)$ $M^2$ $(B)$ $-N^2$ $(C)$ $-M^2$ $(D)$ $M N$

→
Let $A$ be any $3 \times 3$ invertible matrix. Then which one of the following is not always true ?
→
If $f(x) = 4x^8,$ then:
→
Let $A$ be a point on the line $\vec r = \left( {1 - 3\mu } \right)\hat i + \left( {\mu  - 1} \right)\hat j + \left( {2 + 5\mu } \right)\hat k$ and $B(3, 2, 6)$ be a point in the space. Then the value of $\mu $ for which the vector $\overrightarrow {AB} $ is parallel to the plane $x -4y +3z = 1$ is
→
The function $f : A \rightarrow B$ defined by $f(x) = -x^2 + 6x- 8$ is a bijection if,
→
If $f(x) = \frac{{1 - x}}{{1 + x}},$ then $f[f(\cos \;2\theta )] = $
→
$\int\limits_0^{\frac{\pi }{2}} {  {\frac{{4x\sin \,x\, + \,{x^2}\,\cos \,x}}{{2\sqrt {\sin \,x} }}} dx }$ is equal to
→