Download App

7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {\cos x\sqrt {4 - {{\sin }^2}x} } \;dx = $
  • A
    $\frac{1}{2}\sin x\sqrt {4 - {{\sin }^2}x} - 2{\sin ^{ - 1}}\left( {\frac{1}{2}\sin x} \right) + c$
  • ✓
    $\frac{1}{2}\sin x\sqrt {4 - {{\sin }^2}x} + 2{\sin ^{ - 1}}\left( {\frac{1}{2}\sin x} \right) + c$
  • C
    $\frac{1}{2}\sin x\sqrt {4 - {{\sin }^2}x} + {\sin ^{ - 1}}\left( {\frac{1}{2}\sin x} \right) + c$
  • D
    None of these
✓

Answer

Correct option: B.
$\frac{1}{2}\sin x\sqrt {4 - {{\sin }^2}x} + 2{\sin ^{ - 1}}\left( {\frac{1}{2}\sin x} \right) + c$
b
(b) Putting $\sin x = t \Rightarrow \cos x\,dx = dt,$ we get
$\int_{}^{} {\cos x\sqrt {4 - {{\sin }^2}x\,} dx} = \int_{}^{} {\sqrt {4 - {t^2}} dt = \int_{}^{} {\sqrt {{{(2)}^2} - {t^2}} dt} } $
$ = \frac{t}{2}\sqrt {4 - {t^2}} + \frac{4}{2}{\sin ^{ - 1}}\frac{t}{2} + c$
$ = \frac{1}{2}\sin x\sqrt {4 - {{\sin }^2}x} + 2{\sin ^{ - 1}}\left( {\frac{1}{2}\sin x} \right) + 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 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

If $f(x)$ is a polynomial function satisfying the condition $f(x) . f(1/x) = f(x) + f(1/x)$ and $f(2) = 9$ then :
→
Find adjoint of each of the matrices $\left[\begin{array}{ccc}1 & -1 & 2 \\ 2 & 3 & 5 \\ -2 & 0 & 1\end{array}\right]$
→
If $\vec{\text{a}},\ \vec{\text{b}},\ \vec{\text{c}}$ are three non-zero vectors, no two of which are collinear and the vector $\vec{\text{a}}+\vec{\text{b}}$ is collinear with $\vec{\text{c}}$, $\vec{\text{b}}+\vec{\text{c}}$ is collinear with $\vec{\text{a}}$, then $\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}=$
  1. $\vec{\text{a}}$
  2. $\vec{\text{b}}$
  3. $\vec{\text{c}}$
  4. None of these
→
The area bounded by the curve $\text{y}=\sin\text{x}$ between the ordinates $\text{x}=0,\text{x}=\pi$ and the x-axis is:
  1. $2\text{ sq. units}$
  2. $4\text{ sq. units}$
  3. $3\text{ sq. units}$
  4. $1\text{ sq. units}$
→
If the mirror image of the point $\mathrm{P}(3,4,9)$ in the line $\frac{x-1}{3}=\frac{y+1}{2}=\frac{z-2}{1}$ is $(\alpha, \beta, \gamma)$, then $14(\alpha+\beta+\gamma)$ is :
→
Three forces $i + 2\,j - 3\,k,\,\,2\,i + 3\,j + 4\,k$ and $i - j + k$ are acting on a particle at the point $ (0, 1, 2)$ . The magnitude of the moment of the forces about the point $(1,\, - 2,\,0)$ is
→
If $n$ positive integers are taken at random and multiplied together, the probability that the last digit of the product is $2, 4, 6$ or $8$, is
→
At what value of $x,$ will $\left| {\,\begin{array}{*{20}{c}}{x + {\omega ^2}}&\omega &1\\\omega &{{\omega ^2}}&{1 + x}\\1&{x + \omega }&{{\omega ^2}}\end{array}\,} \right| = 0$
→
$\mathop {Lim}\limits_{\lambda  \to 0} \,\,{\left( {\int\limits_0^1 {{{(1 + x)}^\lambda }dx} } \right)^{\frac{1}{\lambda }}}$ is equal to
→
The total revenue in Rupees received from the sale of $x$ units of a product is given by $R (x)=x^2+6 x+5$. The marginal revenue, when $x=20$ is ___________ .
→