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Manipal MET2010MathematicsIndefinite Integration

If f(x) d x=F(x) , then x^3 f (x^2 ) d x is equal to

Options

  1. A1 2 [x^2 F(x) ^2- F(x) ^2 d x ]
  2. B1 2 [x^2 F (x^2 )- F (x^2 ) d (x^2 ) ]
  3. C1 2 [x^2 F(x)- 1 2 F(x) ^2 d x ]
  4. DNone of the above

Correct answer

B. 1 2 [x^2 F (x^2 )- F (x^2 ) d (x^2 ) ]

Step-by-step solution

We have, f(x) d x=F(x) x^3 f (x^2 ) d x= 1 2 x^2 f (x^2 ) d (x^2 )= 1 2 [x^2 F (x^2 )- F (x^2 ) d (x^2 ) ]

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