( ^2 x) , ,dx = ,; ,(x n ,n I) - Vidyadip

MCQ

$\int {\sqrt {({{\sin }^2}x)} } \,\,dx = \,;\,(x \ne n\pi ,n \in I)$

A
$-\cos\, x + c$
B
$\cos \,x + c$
✓
$-\cos\, x \,sgn. (\sin \,x) + c$
D
None of these

✓

Answer

Correct option: C.

$-\cos\, x \,sgn. (\sin \,x) + c$

c
$\int|\sin x| d x$

$=\left\{\begin{array}{l}{\int \sin x d x ; \sin x \geq 0} \\ {-\int \sin x d x ; \sin x<0}\end{array}\right.$

$ = \left\{ {\begin{array}{*{20}{c}}
{\int - \cos x;}&{\sin x \ge 0}\\
{\cos x;}&{\sin x < 0}
\end{array}} \right.$

$ = - \cos x{\mathop{\rm \,\,sgn}} \,(\sin x) + 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

The slope of the tangent to the curve x = t² + 3 t - 8, y = 2t² - 2t - 5 at point (2, -1) is:

$\frac{22}{7}$
$\frac{6}{7}$
$-6$
$\text{None of these}$

What are the direction cosines of a line which is equally inclined to the positive directions of the axes:

If the curve ay + x² = 7 and x³ = y, cut orthogonally at (1, 1), then the value of a is:

The position vectors of $A $ and $ B$ are $i - j + 2k$ and $3i - j + 3k.$ The position vector of the middle point of the line $ AB$ is

Let $P Q R$ be a triangle with $R(-1,4,2)$. Suppose $M(2,1,2)$ is the mid point of $PQ$. The distance of the centroid of $\triangle \mathrm{PQR}$ from the point of intersection of the line $\frac{x-2}{0}=\frac{y}{2}=\frac{z+3}{-1}$ and $\frac{x-1}{1}=\frac{y+3}{-3}=\frac{z+1}{1}$ is

Let $\mathrm{A}=\{1,2,3,4\}$ and $\mathrm{R}=\{(1,2),(2,3),(1,4)\}$ be a relation on $\mathrm{A}$. Let $\mathrm{S}$ be the equivalence relation on $A$ such that $\mathrm{R} \subset \mathrm{S}$ and the number of elements in $\mathrm{S}$ is $\mathrm{n}$. Then, the minimum value of $\mathrm{n}$ is...............

Choose the correct answer from the given four options.
Corner points of the feasible region determined by the system of linear constraints are (0, 3), (1, 1) and (3, 0). Let Z = px + qy, where p, q > 0. Condition on p and q so that the minimum of Z occurs at (3, 0) and (1, 1) is:

p = 2q
$\text{p}=\frac{\text{q}}{2}$
p = 3q
p = q

If $\int {\frac{{\sqrt {1 - {x^2}} }}{{{x^4}}}} dx\, = \,A\,(x)\,{(\sqrt {1 - {x^2}} )^m}\, + \,C,$ for a suitable chosen integer $m$ and a function $A(x),$ where $C$ is a constant of integration, then $(A(x))^m$ equals

Considering only the principal values of the inverse trigonometric functions, the value of $\tan \left(\sin ^{-1}\left(\frac{3}{5}\right)-2 \cos ^{-1}\left(\frac{2}{\sqrt{5}}\right)\right)$

The value of $ \cos { \left( \tan ^{ -1 }{ \tan { 4 } } \right) }$ is-

$ \frac { 1 }{ \sqrt { 17 } }$
$ \frac { 1 }{ \sqrt {- 17 } }$
$ \frac { 1 }{ \sqrt {- 14 } }$
$ -\cos 4$