Download App

INTEGRALS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsINTEGRALS1 Mark
MCQ
Evaluate: $\int\frac{1-\cos\text{x}}{cos\text{x}(1+cos\text{x})}\text{dx}.$
  • ✓
    $\log|\text{sec}\text{x}+\tan\text{x}|-2\tan(\frac{\text{x}}{2})+\text{c}$
  • B
    $\log|\text{sec}\text{x}-\tan\text{x}|-2\tan(\frac{\text{x}}{2})+\text{c}$
  • C
    $\log|\text{sec}\text{x}+\tan\text{x}|+2\tan(\frac{\text{x}}{2})+\text{c}$
  • D
    $\text{None of these}$
✓

Answer

Correct option: A.
$\log|\text{sec}\text{x}+\tan\text{x}|-2\tan(\frac{\text{x}}{2})+\text{c}$
$\log|\text{sec}\text{x}+\tan\text{x}|-2\tan(\frac{\text{x}}{2})+\text{c}$

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 INTEGRALS→INTEGRALS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $\quad E_1=\left\{x \in R : x \neq 1\right.$ and $\left.\frac{x}{x-1}>0\right\}$ and $\quad E_2=\left\{x \in E_1: \sin ^{-1}\left(\log _e\left(\frac{x}{x-1}\right)\right)\right.$ is a real number $\}$.

(Here, the inverse trigonometric function $\sin ^{-1} x$ assumes values in $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ )

Let $f : E _1 \rightarrow R$ be the function defined by $f(x)=\log _c\left(\frac{x}{x-1}\right)$ and $g: E_2 \rightarrow R$ be the function defined by $g(x)=\sin ^{-1}\left(\log _e\left(\frac{x}{x-1}\right)\right)$

 $LIST I$ $LIST II$
$P$ The range of $f$ is $1$ $\left(-\infty, \frac{1}{1- e }\right] \cup\left[\frac{ e }{ e -1}, \infty\right)$
$Q$ The range of $g$ contains $2$ $(0,1)$
$R$ The domain of $f$ contains $3$ $\left[-\frac{1}{2}, \frac{1}{2}\right]$
$S$ The domain of $g$ is $4$ $(-\infty, 0) \cup(0, \infty)$
  $5$ $\left(-\infty, \frac{ e }{ e -1}\right]$
  $6$ $(-\infty, 0) \cup\left(\frac{1}{2}, \frac{ e }{ e -1}\right]$

The correct option is:

→
$\int {\frac{{{{\sin }^8}\,x - {{\cos }^8}\,x}}{{\left( {1 - 2\,{{\sin }^2}\,x\,{{\cos }^2}\,x} \right)}}} dx$ is equal to
→
Let $R$ be the set of all real numbers. The number of continuous functions $f: R \rightarrow R$ such that for all real $x , f( x )+f(2 x )=0$ is
→
If $y = {{\sqrt {a + x} - \sqrt {a - x} } \over {\sqrt {a + x} + \sqrt {a - x} }}$, then ${{dy} \over {dx}} = $
→
$\int\limits^{\infty}_0\log\Big(\text{x}+\frac{1}{\text{x}}\Big)\frac{1}{1+\text{x}^2}\text{ dx}=$
→
$\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}}\sin^9\text{xdx}=$
→
The sum of two non$-$zero number is $8,$ the minimum value of the sum of the reciprohcle is :
→
If ${\tan ^{ - 1}}\frac{{1 - x}}{{1 + x}} = \frac{1}{2}{\tan ^{ - 1}}x$, then $ x =$
→
For what value of $\lambda $, the system of equations $x + y + z = 6,x + 2y + 3z = 10,$ $x + 2y + \lambda z = 12$ is inconsistent  $\lambda =$ ........
→
If $f (x) = e^{-x} + 2 e^{-2x} + 3 e^{- 3x} +...... + \infty$ , then $\int\limits_{\ln 2}^{\ln 3} {f(x)\,dx}  =$
→