Question

${\int }_{\pi /4}^{3\pi /4}|$ cosx $|$ dx $=$

• A. $2-\sqrt{2}$
• B. $2\sqrt{2}$
• C. $\sqrt{2}-1$
• D. $\sqrt{2}+1$

Answer 1

The correct option is A $2-\sqrt{2}$

${\int }_{\frac{\pi }{4}}^{3\frac{\pi }{4}}|cosx|dx$
${\int }_{\frac{\pi }{4}}^{\frac{\pi }{2}}cosxdx-{\int }_{\frac{\pi }{2}}^{3\frac{\pi }{4}}cosxdx$
$sinx{\int }_{\frac{\pi }{4}}^{\frac{\pi }{2}}-sinx{\int }_{\frac{\pi }{2}}^{3\frac{\pi }{4}}$
$(1-\frac{1}{\sqrt{2}})-(\frac{1}{\sqrt{2}}-1)$
$2(1-\frac{1}{\sqrt{2}})=2-\sqrt{2}$