AP EAMCET20226 Jul 2022Morning ShiftMathematicsDefinite IntegrationActual
₀^x x x (3 ^2 x+2 x+ ^3 x-3 ) d x=
Options
- A(5 -12) 4
- B2
- C2 (5 -6)
- D(5 -12) 6
Correct answer
A. (5 -12) 4
Step-by-step solution
aligned & given ₀^ x x (3 ^2 x+2 x+ ^3 x-3 ) d x & ₀^ x x (-3 ^2 x+2 x+ ^3 x ) d x & ₀^ x ( ^2 x-3 x+2 ) d x aligned Let I= ₀^ x ( ^2 x-3 x+2 ) d x ...(1) using propert (a+b-x) I= ₀^ ( -x) ( ^2 x-3 x+2 ) d x ...(ii) adding (1) and (ii) aligned & 2 I= ₀^ ( ^2(x)-3 x+2 ) d x & 2 I= ₀^ ( 1- 2 x 2 -3 x+2 ) d x & 2 I= 2 ₀^ (5- ^2 x-6 x ) d x & I= 4 [5 x- 2 x 2 +6 ^x ]₀^ & = 4 [ (5 x -1 2 2 +6 )-(0-0+6) ] & = 4 [5 6-6] & = 4 [5 -12] aligned