AP EAMCET202420 May 2024Morning ShiftMathematicsDefinite IntegrationActual
_ - ^ x ^3 x 4- ^2 x d x=
Options
- A2 (1- 3)
- B2 (1- 3 4 3 )
- C(1- 3 4 3 )
- D4 (1- 3)
Correct answer
B. 2 (1- 3 4 3 )
Step-by-step solution
I= _ - ^ x ^3 x 4- ^2 x d x I=2 ₀^ x ^3 x 4- ^2 x d x ....(i) I=2 ₀^ ( -x) ^3( -x) 4- ^2( -x) d x I=2 ₀^ ( -x) ^3 x 4- ^2 x d x ....(ii) Adding (i) and (ii) we get, 2 I=2 ₀^ ^3 x 4- ^2 x d x Let x= t - x d x=d t I=- ₁⁻¹ 1-t^2 4-t^2 d t I=2 ₀^1 1-t^2 4-t^2 d tI=2 [ ₀^1 d t-3 ₀^1 1 4-t^2 d t ] I=2 [t- 3 4 | t-2 t+2 | ]₀^1 I=2 [1- 3 4 3 ]