Download App

7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
If $\int_{}^{} {\frac{{dx}}{{1 + \sin x}} = \tan \left( {\frac{x}{2} + a} \right) + b} $, then
  • A
    $a = \frac{\pi }{4},\;b = 3$
  • B
    $a = - \frac{\pi }{4},\;b = 3$
  • C
    $a = \frac{\pi }{4},\;b = $arbitrary constant
  • ✓
    $a = - \frac{\pi }{4},\;b = $arbitrary constant
✓

Answer

Correct option: D.
$a = - \frac{\pi }{4},\;b = $arbitrary constant
d
(d)$\int_{}^{} {\frac{{dx}}{{1 + \sin x}}} = \tan x - \sec x + c = - \frac{{1 - \sin x}}{{\cos x}}$
$ = - \frac{{{{\left( {\cos \frac{x}{2} - \sin \frac{x}{2}} \right)}^2}}}{{{{\cos }^2}\frac{x}{2} - {{\sin }^2}\frac{x}{2}}} + c = - \frac{{1 - \tan \frac{x}{2}}}{{1 + \tan \frac{x}{2}}} + c$
$ = \frac{{\tan \frac{x}{2} - 1}}{{1 + \tan \frac{x}{2}}} + c = \tan \left( {\frac{x}{2} - \frac{\pi }{4}} \right) + c$
$ \Rightarrow a = - \frac{\pi }{4},\,\,b = $ arbitrary constant.

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 7.1 inderfinite integral→7.1 inderfinite integral — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Choose the correct answer from the given four options.
Projection vector of $\vec{\text{a}}$ on $\vec{\text{b}}$ is:
  1. $\bigg(\frac{\vec{\text{a}}\cdot\vec{\text{b}}}{|\vec{\text{b}}|^2}\bigg)\vec{\text{b}}$
  2. $\frac{\vec{\text{a}}\cdot\vec{\text{b}}}{|\vec{\text{b}}|}$
  3. $\frac{\vec{\text{a}}\cdot\vec{\text{b}}}{|\vec{\text{a}}|}$
  4. $\bigg(\frac{\vec{\text{a}}\cdot\vec{\text{b}}}{|\vec{\text{a}}|^2}\bigg)\vec{\text{b}}$
→
If $f(x)$ satisfies the relation $f\left( {\frac{{5x - 3y}}{2}} \right) = \frac{{5f(x) - 3f(y)}}{2}\forall x,y\, \in \,R$ and $f(0)=1, f'(0)=2$ then the period of $sin(f(x))$ is 
→
The function $\text{f}(\text{x})=2\log(\text{x}-2)-\text{x}^2+4\text{x}+1$ increases on the interval:
  1. (1, 2)
  2. (2, 3)
  3. (1, 3)
  4. (2, 4)
→
The linear inequalities or equations or restrictions on the variables of a linear programming problem are called:
  1. A constraint
  2. Decision variables
  3. Objective function
  4. None of the above
→
If three conterminous edges of a parallelopiped are represented by $a - b,\,\,b - c$ and $c - a$, then its volume is
→
Find the value of p for which the points (−5, 1), (1, p) and (4, −2) are collinear.
  1. 1
  2. 0
  3. −1
  4. 2
→
Let $A=\left[\begin{array}{llc}2 & 1 & 2 \\ 6 & 2 & 11 \\ 3 & 3 & 2\end{array}\right]$ and $P=\left[\begin{array}{lll}1 & 2 & 0 \\ 5 & 0 & 2 \\ 7 & 1 & 5\end{array}\right]$. The sum of the prime factors of $\left|\mathrm{P}^{-1} \mathrm{AP}-2 \mathrm{I}\right|$ is equal to
→
Consider the function $\mathrm{f}:(0,2) \rightarrow \mathrm{R}$ defined by $f(x)=\frac{x}{2}+\frac{2}{x}$ and the function$ g(x)$ defined by $g(x)=\left\{\begin{array}{cc}\min \{f(t)\}, & 0 < t \leq x \text { and } 0 < x \leq 1 \\ \frac{3}{2}+x, & 1 < x< 2\end{array}\right.$. Then
→
The value of the determinant $\begin{vmatrix}\text{a}-\text{b}&\text{b}+\text{c}&\text{c}\\\text{b}-\text{c}&\text{c}+\text{b}&\text{b}\\\text{c}+\text{a}&\text{a}+\text{b}&\text{c}\end{vmatrix}$ is:
  1. a3 + b3 + c3
  2. 3bc
  3. a3 + b3 + c3 - 3abc
  4. None of these
→
The population $p (t)$ at time $t$ of a certain mouse species satisfies the differential equation $\frac{{dp\left( t \right)}}{{dt}} = 0.5p\left( t \right) - 450$ . If $p\left( 0 \right) = 850$ then the time at which the population becomes zero is :
→