AP EAMCET20224 Jul 2022Evening ShiftMathematicsIndefinite IntegrationActual
If ∫ 1 + tan x sin 2 x d x = A logtan x + B tan x + C then 4 A - B =
Options
- A- 1
- B2
- C1
- D- 2
Correct answer
C. 1
Step-by-step solution
I = ∫ 1 + tan x sin 2 x d x = ∫ 1 sin 2 x + tan x sin 2 x d x = ∫ 1 2 sin x cos x d x + ∫ sin x 2 sin x cos x cos x d x = ∫ 1 2 sin x cos x cos 2 x d x + ∫ 1 2 sin x cos x cos 2 x d x = ∫ sec 2 x 2 tan x d x + ∫ sec 2 x 2 tan x d x = 1 2 ln tan x + tan x + C So, 4 A - B = 4 × 1 2 - 1 = 1