_ - a ^a x ,f( x) ,dx = - Vidyadip

MCQ

$\int_{ - a}^a {\sin x\,f(\cos x)\,dx = } $

A
$2\int_0^a {\sin x\,f(\cos x)\,dx} $
✓
$0$
C
$1$
D
None of these

✓

Answer

Correct option: B.

$0$

b
(b) $I = \int_{ - a}^a {\sin xf(\cos x)\,dx} $

$f(x) = \sin x\,f(\cos x) \Rightarrow f( - x) = - \sin x\,f(\cos x)$

$\because \,\,\,\,f(x)$ is an odd function

$\therefore \,\,\,I = \int_{}^{} {f(x)dx = 0} $.

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 7.2 definite integral→7.2 definite integral — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $"A"$ he the area bounded by the curve $y = {\cos ^{ - 1}}\sqrt {1 - {x^2}}$ , tangent to the curve $y = {\sin ^{ - 1}}x$ at $x = 0$ and the line $x = 1$ then the value of $2 (\{A\} + sgn (A))$ is ( where $\{.\}$ is a fractional patfunction and $sgnx$ is signum function )

The function $\text{f(x)}=|\cos\text{x}|$ is:

Differentiable at$\text{x}=(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}$
Continuous but not differentiable at $\text{x}=(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}$
Neither differentiable nor continuous at $\text{x}=\text{n}\in\text{Z}$
None of these.

Linear programming used to optimize mathematical procedure and is:

Solution of differential equation x dy - yx = 0 represents:

rectangular hyperbola
straight line passing through origin
parabola whose vertex is at origin
circle whose center is at origin

A relation R is defined from {2, 3, 4, 5} to {3, 6, 7, 10} by : xRy ⇔ x is relatively prime to y. Then, domain of R is:

{2, 3, 5}
{3, 5}
{2, 3, 4}
{2, 3, 4, 5}

Choose the correct answer from the given four options:
The area of the region bounded by the curve x² = 4y and the straight line x = 4y - 2 is:

$\frac{3}{8}\text{ sq. units}$
$\frac{5}{8}\text{ sq. units}$
$\frac{7}{8}\text{ sq. units}$
$\frac{9}{8}\text{ sq. units}$

Let $[x]$ denotes the greatest integer less than or equal to $x$. If $f(x) = [x\sin \pi x]$, then $f(x)$ is

A particle acted on by two forces $3i + 2j - 3k$ and $2i + 4j + 2k$ is displaced from the point $i + 2j + k$ to $5i + 4j + 2k.$ The total work done by the forces is equal to ............ $\mathrm{unit}$

Given : $f(x)=\left\{\begin{array}{ccc}{x} & {,} & {0 \leq x < \frac{1}{2}} \\ {\frac{1}{2}} & {,} & {x=\frac{1}{2}} \\ {1-x} & {,} & {\frac{1}{2} < x \leq 1}\end{array}\right.$

and $g(x)=\left(x-\frac{1}{2}\right)^{2}, x \in R .$ Then the area (in sq. units) of the region bounded by the curves, $y=f(x)$ and $y=g(x)$ between the lines, $2 \mathrm{x}=1$ and $2 \mathrm{x}=\sqrt{3},$ is

Direction cosines of ray from P(1, −2, 4) to Q(−1, 1, −2) are: