JEE Main20241 Feb 2024Evening ShiftMathematicsDefinite IntegrationActual
The value of ∫ 0 1 2 x 3 − 3 x 2 − x + 1 1 3 d x is equal to:
Options
- A0
- B1
- C2
- D- 1
Correct answer
A. 0
Step-by-step solution
I = ∫ 0 1 2 x 3 − 3 x 2 − x + 1 1 3 d x Using ∫ 0 2 a f x d x = 0 when f 2 a − x = − f x Now, finding f 1 - x we get, ⇒ I = ∫ 0 1 2 1 - x 3 − 3 1 - x 2 − 1 - x + 1 1 3 d x ⇒ I = ∫ 0 1 2 1 - x 3 - 3 x + 3 x 2 − 3 1 + x 2 - 2 x 2 − 1 - x + 1 1 3 d x ⇒ I = ∫ 0 1 2 - 2 x 3 - 6 x + 6 x 2 - 3 - 3 x 2 + 6 x − 1 + x + 1 1 3 d x ⇒ I = ∫ 0 1 - 2 x 3 + 3 x 2 + x - 1 1 3 d x ⇒ I = - I ⇒ f 1 − x = − f x ∴ I = 0