Download App

7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
$\int\limits_{\pi /2}^\pi  {\,\frac{{1 - \sin x}}{{1 - \cos x}}} $ $dx =$
  • ✓
    $1 - ln 2$
  • B
    $ln 2$
  • C
    $1 + ln 2$
  • D
    $none$
✓

Answer

Correct option: A.
$1 - ln 2$
a
$I\,\, = \,\int {\frac{{1 - \sin x}}{{2{{\sin }^2}\frac{x}{2}}}\,\,\,\,dx} $= $\int {\left( {\frac{1}{2}\,\cos e{c^2}\frac{x}{2} - \cot \frac{x}{2}} \right)\,dx} $ $= -x cot$$\left. {\frac{x}{2}} \right|_{\,\frac{\pi }{2}}^{\,\pi }$

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

Let $f: R \rightarrow R$ be a function defined by $f(x)=\left\{\begin{array}{cc}{[x],} & x \leq 2 \\ 0, & x>2\end{array}\right.$, where $[x]$ is the greatest integer less than or equal to $x$. If $I=\int_{-1}^2 \frac{x f\left(x^2\right)}{2+f(x+1)} d x$, then the value of $(4 I-1)$ is
→
If $a,b,c$ are respectively the ${p^{th}},{q^{th}}{r^{th}}$terms of an $A.P.,$ the $\left| {\,\begin{array}{*{20}{c}}a&p&1\\b&q&1\\c&r&1\end{array}\,} \right| = $
→
If $\text{f}(\text{x})=\text{e}^{\text{x}}\sin\text{x}$ in $[0,\pi],$ then c in Rolle's theorem is:
  1. $\frac{\pi}{6}$
  2. $\frac{\pi}{4}$
  3. $\frac{\pi}{2}$
  4. $\frac{3\pi}{4}$
→
If A and B are two matrices of order 3×m and 3×n respectively and m = n, then the order of 5A - 2B is:
  1. m×3
  2. 3×3
  3. m×n
  4. 3×n
→
If $\vec x$ is a unit vector such that $\vec x \times \left( {\hat i - 2\hat j + \hat k} \right) =  - \hat i + \hat k$ , then $\vec x$ is 
→
If $(1 -x + 2x^2)^n$ = $a_0 + a_1x + a_2x^2+..... a_{2n}x^{2n}$ , $n \in N$ , $x \in R$ and $a_0$ , $a_2$ and $a_1$ are in $A$ . $P$ .,then there exists 
→
The number of distinct real roots of the equation $3 x^{4}+4 x^{3}-12 x^{2}+4=0$ is ..... .
→
The population $P = P ( t )$ at time ${ }^{\prime} t ^{\prime}$ of a certain species follows the differential equation $\frac{ dP }{ dt }=0.5 P -450 .$ If $P (0)=850,$ then the time at which population becomes zero is
→
The Polygon Law of Vector Addition is simply an extension of ____________?
  1. Parallelogram Law of Vector Addition
  2. Triangular Law of Vector Addition
  3. Both A and B
  4. None of the above
→
The solution of the equation $\frac{{dy}}{{dx}} + y\tan x = {x^m}\cos x$ is
→