Question

If $g\left(x\right)=\underset{0}{\overset{x}{\int }}\cos \left(4t\right)dt$, then $g(x+\pi )$ equals

• A. $g\left(x\right)\cdot g\left(\pi \right)$
• B. $g\left(x\right)+g\left(\pi \right)$
• C. $\frac{g\left(x\right)}{g\left(\pi \right)}$
• D. $g\left(x\right)-g\left(\pi \right)$

Answer 1

The correct option is B $g\left(x\right)+g\left(\pi \right)$

$g\left(x\right)=\underset{0}{\overset{x}{\int }}\cos \left(4t\right)dt$
$\Rightarrow g\left(x\right)=\frac{\sin 4x}{4}$
$\because g\left(0\right)=0$ $\therefore g(x+\pi )=g\left(x\right)+g\left(\pi \right)$ or $g(x+\pi )=g\left(x\right)-g\left(\pi \right)$

$\left(B\right)$ and $\left(C\right)$ both are correct.

BONUS