Question

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

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

Answer 1

Answer: (B), (C)

$ g\left(x\right) = \int\limits^{x+\pi}_{0}$ cos 4t dt, $= g\left(x\right) +\int\limits^{\pi}_{0}$ cos 4t dt
$= g\left(x\right) + g\left(\pi\right)$
Here $g\left(\pi\right) = \int\limits^{\pi}_{0}$cos 4t dt $= 0$
so answers are $\left(2\right)$ or $\left(3\right)$