Download App

STD 12 - 7.1 inderfinite integral — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 7.1 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 STD 12 - 7.1 inderfinite integral→STD 12 - 7.1 inderfinite integral — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Let $F: R \rightarrow R$ be a thrice differentiable function. Suppose that $F (1)=0, F (3)=-4$ and $F^{\prime}( x )<0$ for all $x \in$ $(1 / 2,3)$. Let $f(x)=x F(x)$ for all $x \in R$.

$1.$ The correct statement$(s)$ is(are)

$(A)$ $f^{\prime}(1) < 0$

$(B)$ $f(2) < 0$

$(C)$ $f^{\prime}(x) \neq 0$ for any $x \in(1,3)$

$(D)$ $f^{\prime}(x)=0$ for some $x \in(1,3)$

$2.$ If $\int_1^3 x^2 F^{\prime}(x) d x=-12$ and $\int_1^3 x^3 F^{\prime \prime}(x) d x=40$, then the correct expression$(s)$ is(are)

$(A)$ $9 f^{\prime}(3)+f^{\prime}(1)-32=0$

$(B)$ $\int_1^3 f(x) d x=12$

$(C)$ $9 f^{\prime}(3)-f^{\prime}(1)+32=0$

$(D)$ $\int_1^3 f(x) d x=-12$

Give the answer question $1$ and $2.$

→
If $\left| {\,\begin{array}{*{20}{c}}a&b&0\\0&a&b\\b&0&a\end{array}\,} \right| = 0$, then
→
Choose the correct answers from the given four options:
If $\text{y}=\log\Big(\frac{1-\text{x}^2}{1+\text{x}^2}\Big),$ then $\frac{\text{dy}}{\text{dx}}$ is equal to:
→
The diameter of a circle is increasing at the rate of 1cm/sec. When its radius is $\pi$ the rate of increase of its area is:
→
The order and the degree of the differential equation $\left(1+3 \frac{d y}{d x}\right)^2=4 \frac{d^3 y}{d x^3}$ respectively, are
→
If $x = {{3at} \over {1 + {t^3}}},y = {{3a{t^2}} \over {1 + {t^3}}},$ then ${{dy} \over {dx}} =$
→
If $x^{3} d y+x y d x=x^{2} d y+2 y d x ; y(2)=e$ and $x$ $>1,$ then $y (4)$ is equal to
→
The point on the curve $y^2 = 4x$ which is nearest to, the point $(2, 1)$ is :
→
For $x \in R$, two real valued functions $f(x)$ and $g(x)$ are such that, $g(x)=\sqrt{x}+1$ and $f o g(x)=x+3-\sqrt{x}$. Then $f(0)$ is equal to
→
Let $M$ denotes set of all $3 \times 3$ non singular matrices. Define the relation $R$ by

$R = \{ (A,B) \in M \times M$ : $AB = BA\} ,$ then $R$ is-

→