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KCET2008MathematicsIndefinite Integration

If f(x) d x=g(x) , then f(x) g(x) d x is equal to

Options

  1. A1 2 f ²( x )
  2. B1 2 g²(x)
  3. C1 2 [g^ (x) ]²
  4. Df^ (x) g(x)

Correct answer

B. 1 2 g²(x)

Step-by-step solution

Given, f(x) d x=g(x)- [g^ (x) f(x) d x ] d x =g(x) g(x)- g^ (x) g(x) d x aligned &=[g(x)]²- [g(x)]² 2 &= g²(x) 2 aligned

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