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AP EAMCET2015MathematicsIndefinite Integration

f(x) g^ (x)-f^ (x) g(x) f(x) g(x) [ g(x)- f(x)] d x is equal to

Options

  1. A[ g(x) f(x) ]+C
  2. B1 2 [ g(x) f(x) ]^2+C
  3. Cg(x) f(x) [ g(x) f(x) ]+C
  4. D[ g(x) f(x) ]- g(x) f(x) +C

Correct answer

B. 1 2 [ g(x) f(x) ]^2+C

Step-by-step solution

Let I= f(x) g^ (x)-f^ (x) g(x) f(x) g(x) aligned & [ g(x)- f(x)] d x & = [ g(x) f(x) ] d g(x) f(x) aligned Put t= [ g(x) f(x) ]d t=d ( [ g(x) f(x) ] ) Now, I= t d t= t^2 2 +C= 1 2 g(x) f(x) ^2+C

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