MHT CET202210 Aug 2022Morning ShiftMathematicsIndefinite IntegrationActual
4 x^2 ⁻¹ (x^3 ) 1+x^6 ~d x= (where C is a constant of integration.)
Options
- A-2 3 ( ⁻¹ X^3 )+C
- B-2 3 ( ⁻¹ X^3 )^2+C
- C2 3 ( ⁻¹ x^3 )+C
- D2 3 ( ⁻¹ x^3 )^2+C
Correct answer
B. -2 3 ( ⁻¹ X^3 )^2+C
Step-by-step solution
4 x^2 ⁻¹ (x^3 ) 1+x^6 ~d x let ⁻¹ (x^3 )=t then -3 x^2 1+x^6 d x=d t aligned & =- 4 3 t ~d t & =- 4 3 t^2 2 +c=- 2 3 ( ⁻¹ X^3 )^2+c aligned