AP EAMCET202423 May 2024Morning ShiftMathematicsDefinite IntegrationActual
If ₀^ x x 4 ^2 x+3 ^2 x d x=
Options
- A^2 6 3
- B3 3
- C^2 3 3
- D3 ^2
Correct answer
A. ^2 6 3
Step-by-step solution
I= ₀^ x x 4 ^2 x+3 ^2 x d x I= ₀^ x x ^2 x+3 d x ....(i) I= ₀^ ( -x) x ^2 x+3 d x ....(ii) Adding (i) and (ii) 2 I= ₀^ x ^2 x+3 d x Let x=t - x d x=d t aligned & 2 I=- ₁⁻¹ 1 t^2+3 d t 2 I=- _ -1 ^1 1 t^2+3 d t & 2 I= 3 [ ⁻¹ t 3 ]_ -1 ^1 & 2 I= 3 [ 6 + 6 ] I= ^2 6 3 aligned