Question

If g(x) = ${\int }_0^x$ cos 4 tdt, then g(x +$\pi$ ) equals

• A. $g\left(x\right)$
• B. $g\left(x\right).g\left(\pi \right)$
• C. $\frac{g\left(x\right)}{g\left(\pi \right)}$
• D. None of these

Answer 1

The correct option is A $g\left(x\right)$

$g\left(x\right)={\int }_0^{x}cos4tdt={\left[\frac{sin4t}{4}\right]}_0^x=\frac{sin4x}{4}$
$g(x+\pi )=\frac{sin\left(4\right(x+\pi \left)\right)}{4}=\frac{sin4x}{4}=g\left(x\right)$