Question

Evaluate the definite integrals.
${\int }_0^{\frac{\pi }{2}}cos2xdx.$

Answer 1

${\int }_0^{\frac{\pi }{2}}cos2xdx={\left[\frac{sin2x}{2}\right]}_0^{\frac{\pi }{2}}(\because \int cosaxdx=\frac{sinax}{a})=\frac{1}{2}[sin2x{]}_0^{\frac{\pi }{2}}=\frac{1}{2}[(sin2\times \frac{\pi }{2})-sin(0\left)\right]=\frac{1}{2}[0-0]=0$