MHT CET202415 May 2024Morning ShiftMathematicsIndefinite IntegrationActual
The value of x x 9-16 ^2 x ~d x is equal to
Options
- A1 24 ( 5+4 x 5-4 x )+ c , (where c is a constant of integration)
- B1 40 ( 5+4 x 5-4 x )+ c , (where c is a constant of integration)
- C1 24 ( 5-4 x 5+4 x )+ c , (where c is a constant of integration)
- D1 40 ( 5-4 x 5+4 x )+ c , (where c is a constant of integration)
Correct answer
B. 1 40 ( 5+4 x 5-4 x )+ c , (where c is a constant of integration)
Step-by-step solution
Let I aligned I & = x x 9-16 ^2 x ~d x & = x x 9-16 ( ^2 x-1 ) d x & = x x 25-16 ^2 x ~d x aligned Put x= t x x ~d x= dt aligned I & = dt 5^2-(4 t )^2 & = 1 2(5) 1 4 | 5+4 t 5-4 t | & = 1 40 | 5+4 x 5-4 x |+ c aligned