MHT CET202313 May 2023Morning ShiftMathematicsIndefinite IntegrationActual
If I = 2 x-7 3 x-2 ~d x , then I is given by
Options
- A106 27 (3 x-2)^ 3 2 + c , where c is a constant of integration.
- B98 27 (3 x-2)^ 3 2 + c , where c is a constant of integration.
- C4 27 (3 x-2)^ 3 2 - 34 9 (3 x-2)^ 1 2 + c , where c is a constant of integration.
- D4 27 (3 x-2)^ 3 2 + 34 9 (3 x-2)^ 1 2 + c , where c is a constant of integration
Correct answer
C. 4 27 (3 x-2)^ 3 2 - 34 9 (3 x-2)^ 1 2 + c , where c is a constant of integration.
Step-by-step solution
aligned I & = 2 x-7 3 x-2 ~d x & = 2 3 (3 x-2)- 17 3 3 x-2 ~d x & = 2 3 (3 x-2)^ 1 2 ~d x- 17 3 (3 x-2)^ -1 2 ~d x & = 2 3 (3 x-2)^ 3 2 3 2 1 3 - 17 3 (3 x-2)^ 1 2 1 2 1 3 + c & = 4 27 (3 x-2)^ 3 2 - 34 9 (3 x-2)^ 1 2 + c aligned