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MHT CET20249 May 2024Morning ShiftMathematicsIndefinite IntegrationActual

If f (x) d x= (x) , then x^5 f (x^3 ) d x is equal to

Options

  1. A1 3 x^3 (x^3 )-3 x^3 (x^3 ) d x+ c , (where c is a constant of integration)
  2. B1 3 (x^3 (x^3 )- x^3 (x^3 ) d x )+ c , (where c is a constant of integration)
  3. C1 3 x^3 (x^3 )- x^2 (x^3 ) d x+ c , (where c is a constant of integration)
  4. D1 3 (x^3 (x^3 )- x^2 (x^3 ) d x )+ c , (where c is a constant of integration)

Correct answer

C. 1 3 x^3 (x^3 )- x^2 (x^3 ) d x+ c , (where c is a constant of integration)

Step-by-step solution

f (x) d x= (x) Consider aligned I & = x^5 f (x^3 ) d x & = x^3 x^2 f (x^3 ) d x aligned Let x^3= t 3 x^2 ~d x= dt aligned & = t 3 f ( t ) dt & = 1 3 t f( t ) dt & = 1 3 [ t f ( t ) dt - d dt ( t ) f ( t ) dt ] & = 1 3 [ t ( t )- ( t ) dt ]+ c & = 1 3 (x^3 (x^3 ) )- (x^3 ) x^2 ~d x+ c aligned

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