Question

The value of $I = \int _ { 0 } ^ { \pi / 2 } \frac { ( \sin x + \cos x ) ^ { 2 } } { \sqrt { 1 + \sin 2 x } } d x$is

• A. 3
• B. 1
• C. 2
• D. 0

Answer 1

Answer: (C)

2

Answer 2

$= \int _ { 0 } ^ { \pi / 2 } \frac { ( \sin x + \cos x ) ^ { 2 } } { \sqrt { ( \sin x + \cos x ) ^ { 2 } } } d x$

$I = \int _ { 0 } ^ { \pi / 2 } ( \sin x + \cos x ) d x = ( - \cos x + \sin x ) _ { 0 } ^ { \pi / 2 }$

$I = 1 - ( - 1 ) = 2$.