JEE Main20211 Sep 2021Evening ShiftMathematicsArea Under CurvesActual
The area, enclosed by the curves y = sin x + cos x and y = | cos x - sin x | and the lines x = 0 , x = π 2 , is :
Options
- A2 2 ( 2 + 1 )
- B2 2 ( 2 - 1 )
- C4 ( 2 - 1 )
- D2 ( 2 + 1 )
Correct answer
B. 2 2 ( 2 - 1 )
Step-by-step solution
A = ∫ 0 π / 2 ( ( cos x + sin x ) - | cos x - sin x | ) d x A = ∫ 0 π / 4 ( ( cos x + sin x ) - ( cos x - sin x ) ) d x + ∫ π / 4 π / 2 ( ( cos x + sin x ) - ( sin x - cos x ) ) d x A = 2 ∫ 0 π / 4 sin x d x + 2 ∫ π / 4 π / 2 cos x d x = 2 - 1 2 + 1 + 2 1 - 1 2 = 4 - 2 2 = 2 2 ( 2 - 1 )