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MHT CET202415 May 2024Morning ShiftMathematicsIndefinite IntegrationActual

The value of x x 9-16 ^2 x ~d x is equal to

Options

  1. A1 24 ( 5+4 x 5-4 x )+ c , (where c is a constant of integration)
  2. B1 40 ( 5+4 x 5-4 x )+ c , (where c is a constant of integration)
  3. C1 24 ( 5-4 x 5+4 x )+ c , (where c is a constant of integration)
  4. 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

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