Question

The value of the integral is $I={\int }_0^{\pi /4}co{s}^{2}xdx$

• A. $\frac{\pi }{8}+\frac{1}{4}$
• B. $\frac{\pi }{8}-\frac{1}{4}$
• C. $-\frac{\pi }{8}-\frac{1}{4}$
• D. $-\frac{\pi }{8}+\frac{1}{4}$

Answer 1

The correct option is A $\frac{\pi }{8}+\frac{1}{4}$

$I={\int }_0^{\pi /4}co{s}^{2}xdx$
$={\int }_0^{\pi /2}\left(\frac{1+cos2x}{2}\right)dx$
$={[\frac{x}{2}+\frac{sin2x}{4}]}_0^{\pi /4}$
$=\frac{\pi }{8}+\frac{1}{4}$