If $g(x)=\int_0^x \cos 4 t ~d t$, then $g(x+\pi)$ equals

Question

Aicharya · Accepted Answer

$g(x)=\int_0^x \cos 4 t ~d t$ $\Rightarrow g^{\prime}(x)=\cos 4 x \quad \Rightarrow g(x)=\frac{\sin 4 x}{4}+k \quad \Rightarrow g(x)=\frac{\sin 4 x}{4}[\because g(0)=0]$ $g(x+\pi)=g(x)+g(\pi)=g(x)-g(\pi)(\because g(\pi)=0)$

If $g(x)=\int_0^x \cos 4 t ~d t$, then $g(x+\pi)$ equals

Solution