MHT CET202613 April 2026Evening ShiftMathematicsIndefinite IntegrationActual
1+ x ,dx is equal to
Options
- A2 2 ( x 2 - 4 ) + c
- B2 2 ( x 2 + 4 ) + c
- C2 ( x 2 - 4 ) + c
- D2 ( x 2 + 4 ) + c
Correct answer
A. 2 2 ( x 2 - 4 ) + c
Step-by-step solution
I = 1+ x ,dx Using the trigonometric identities ^2 ( x 2 ) + ^2 ( x 2 ) = 1 and x = 2 ( x 2 ) ( x 2 ) , we get: 1 + x = ^2 ( x 2 ) + ^2 ( x 2 ) + 2 ( x 2 ) ( x 2 ) = ( ( x 2 ) + ( x 2 ) )^2 Substituting this into the integral: I = ( ( x 2 ) + ( x 2 ) ) ,dx Integrating term by term: I = -2 ( x 2 ) + 2 ( x 2 ) + c I = 2 ( ( x 2 ) - ( x 2 ) ) + c Multiplying and dividing by 2 : I = 2 2 ( ( x 2 ) 1 2 - ( x 2 ) 1 2 ) + c I = 2 2 ( ( x 2 ) ( 4 ) - ( x 2 ) ( 4 ) ) + c Using the identity (A - B) = A B - A B : I = 2 2 ( x 2