Question

${\int }_0^{10x}|\sin x|dx=$ ____

• A. $20$
• B. $8$
• C. $10$
• D. $18$

Answer 1

The correct option is A $20$

The value of the given definite integral is
$I={\int }_0^{10\pi }|\sin x|dx$
$=10{\int }_0^{\pi }|\sin x|dx$
$[\because |\sin x|]$ is periodic with period $\pi )$
$=10{\int }_0^{\pi }\sin xdx$
$[\because \sin x>0\text{in interval}(0,\pi \left)\right]$

This can be further simplified as
$I=20{\int }_0^{\frac{\pi }{2}}\sin xdx$
$[\because \sin (\pi -x)=\sin x]$
$=20[-\cos x{]}_0^{\frac{\pi }{2}}=20$