Question

Area bounded by one arch of the curve $y=sinmx(m>0)$ and the $x-axis$ is

• A. $2/m$
• B. $2$
• C. $2m$
• D. $1/m$

Answer 1

The correct option is A $2/m$

$y=\sin mx$

$A={\int }_0^{\pi }\sin mxdx$

$=\frac{1}{m}{[-\cos mx]}_0^{\pi }$

$=\frac{1}{m}[-\cos m\pi +\cos 0]$

$=\frac{1}{m}[-(-1)+1]$

$=\frac{2}{m}$

$\therefore$ Area bounded by one each of the curve $y=\sin mx(m>0)$ & x-axis is $\frac{2}{m}$.