If g ( x ) = _0^x 4t ;dt then g ( x + ) = - Vidyadip

MCQ

If $g\left( x \right) = \mathop \smallint \limits_0^x \cos 4t\;dt$ then $g\left( {x + \pi } \right) = $

A
$\frac{{g\left( x \right)}}{{g\left( \pi \right)}}$
B
$g\left( x \right) + g\left( \pi \right)$
C
$g\left( x \right) - g\left( \pi \right)$
✓
$(b) $ and $(c)$ both

✓

Answer

Correct option: D.

$(b) $ and $(c)$ both

d
$(a,d):g(x) = \int\limits_0^x {\cos 4tdt} $

$\Rightarrow g(x)=\left[\frac{\sin 4 t}{4}\right]_{0}^{x}=\frac{\sin 4 x}{4}$

$\Rightarrow g(x+\pi)=\frac{\sin 4(x+\pi)}{4}=\frac{\sin 4 x}{4}$

$\Rightarrow g(\pi)=0 \Rightarrow g(x+\pi)=g(x)+g(\pi) \text { or } g(x)-g(\pi)$

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 - 7.2 definite integral→STD 12 - 7.2 definite 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 $A = R – \{3\}, B = R – \{1\}.$ Let $f : A \rightarrow B$ be defined by $\text{f(x)}=\frac{\text{x}-2}{\text{x}-3}.$ Then,

The value of f(0), so that the function $\text{f(x)}=\frac{\sqrt{\text{a}^2+\text{ax+x}^2}-\sqrt{\text{a}^2+\text{ax+x}^2}{}}{\sqrt{\text{a+x}}-\sqrt{\text{a-x}}}$ becomes continuous for all x, given by:

Let $f:[0,1] \rightarrow R$ be an injective continuous function that satisifes the condition $-1 < f(0) < f(1) < 1$

Then, the number of functions $g:[-1,1] \rightarrow[0,1]$ such that $(g \circ f)(x)=x$ for all $x \in[0,1]$ is

A bag contains 5 red and 3 blue balls are drawn at random without replacement, then the probability of getting exactly one red ball is.

Let $S=\left\{x \in R: 0 < x < 1\right.$ and $\left.2 \tan ^{-1}\left(\frac{1-x}{1+x}\right)=\cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right)\right\}$. If $n ( S )$ denotes the number of elements in $S$ then:

Let $f(\mathrm{x})=\left\{\begin{array}{cl}-\mathrm{a} & \text { if }-\mathrm{a} \leq \mathrm{x} \leq 0 \\ \mathrm{x}+\mathrm{a} & \text { if } 0<\mathrm{x} \leq \mathrm{a}\end{array}\right.$ where $\mathrm{a}>0$ and $\mathrm{g}(\mathrm{x})=(f|\mathrm{x}|)-|f(\mathrm{x})|) / 2$. Then the function $\mathrm{g}:[-\mathrm{a}, \mathrm{a}] \rightarrow[-\mathrm{a}, \mathrm{a}]$ is

If $y=x \log _e x$ then value of $\frac{d^2 y}{d x^2}$ :

The sine and cosine curves intersects infinitely many times giving bounded regions of equal areas. The area of one of such region is

If $\text{y}=\text{a}+\text{bx}^2,\text{a,b}$ arbitrary constants, then

The function$\text{f(x)}=1+|\cos\text{x}|$ is: