JEE Main20208 Jan 2020Evening ShiftMathematicsDefinite IntegrationActual
If I = ∫ 1 2 d x 2 x 3 - 9 x 2 + 12 x + 4 , then
Options
- A1 8 < I 2 < 1 4
- B1 9 < I 2 < 1 8
- C1 16 < I 2 < 1 9
- D1 6 < I 2 < 1 2
Correct answer
B. 1 9 < I 2 < 1 8
Step-by-step solution
f x = 1 2 x 3 - 9 x 2 + 12 x + 4 f ' x = - 1 2 6 x 2 - 18 x + 12 2 x 3 - 9 x 2 + 12 x + 4 3 2 f ' x = - 6 x - 1 x - 2 2 2 x 3 - 9 x 2 + 12 x + 4 3 2 f ' x = 0   ⇒ x = 1 ,   2 f 1 = 1 3 , f 2 = 1 8 1 3 < f x < 1 8 ⇒ ∫ 1 2 1 3 d x < ∫ 1 2 f x d x < ∫ 1 2 1 8 d x ⇒ 1 3 < I < 1 8   ⇒ 1 9 < I 2 < 1 8 .