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COMEDK2019MathematicsIndefinite Integration

If f(x) d x=g(x) , then f(x) g(x) d x=

Options

  1. A1 2 f²(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

We have, f(x) d x=g(x) f(x)=g^ (x) Now, let I= f(x) g(x) d x= g^ (x) g(x) d x Put g(x)=t g^ (x) d x=d t I= t d t= t² 2 +C= 1 2 (g(x))²+C

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