AP EAMCET20224 Jul 2022Evening ShiftMathematicsDefinite IntegrationActual
If f x = Max sin x , cos x and g x = Min sin x , cos x , then ∫ 0 π f x d x + ∫ 0 π g x d x =
Options
- A2 2 + 2
- B2 2 - 2
- C2
- D2 2
Correct answer
C. 2
Step-by-step solution
Given f x = Max sin x , cos x and g x = Min sin x , cos x ∫ 0 π f x d x + ∫ 0 π g x d x = ∫ 0 π 4 sin x d x + ∫ π 4 π cos x d x + ∫ 0 π 4 cos x d x + ∫ π 4 π sin x d x = - cos x 0 π 4 + sin x π 4 π + sin x 0 π 4 + - cos x π 4 π = - 1 2 + 1 + 0 - 1 2 + 1 2 - 0 + 1 + 1 2 = 2