AP EAMCET202022 Sep 2020Morning ShiftMathematicsIndefinite IntegrationActual
x- x 5+ (2 x) d x=
Options
- A1 2 ⁻¹ [ 1 2 ( x+ x) ]+c
- B1 2 ⁻¹ [ 1 2 ( x+ x) ]+c
- C1 2 ⁻¹ [ 1 2 ( x+ x) ]+c
- D1 2 ⁻¹ [ 1 2 ( x+ x) ]+c
Correct answer
B. 1 2 ⁻¹ [ 1 2 ( x+ x) ]+c
Step-by-step solution
aligned I & = x- x 5+ 2 x d x & = x- x 4+( x+ x)^2 d x aligned Let x+ x=t ( x- x) d x=d t aligned I & = d t 4+t^2 = 1 2 ⁻¹ ( t 2 )+C & = 1 2 ⁻¹ ( x+ x 2 )+C aligned