MHT CET202521 Apr 2025Evening ShiftMathematicsIndefinite IntegrationActual
( x 16 ) ( x 8 ) ( x 4 ) ( x 16 ) dx =
Options
- A16 x 256 +c , where c is the constant of integration
- B- 16 x 256 +c , where c is the constant of integration
- C16 x 256 +c, where c is the constant of integration
- D- ( x 2 ) 4 +c , where c is the constant of integration
Correct answer
D. - ( x 2 ) 4 +c , where c is the constant of integration
Step-by-step solution
The integral is evaluated by applying the identity = 1 2 (2 ) repeatedly. Combining ( x 16 ) ( x 16 ) yields 1 2 ( x 8 ) . Combining ( x 8 ) ( x 8 ) yields 1 2 ( x 4 ) . The remaining product becomes 1 4 ( x 4 ) ( x 4 ) , dx , and combining these gives 1 8 ( x 2 ) , dx . Integration yields - 1 4 ( x 2 ) + c , matching option D .