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} $

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

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

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

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