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AP EAMCET20226 Jul 2022Morning ShiftMathematicsIndefinite IntegrationActual

If e^x (f(x)-f^ (x) )=g(x)+C , then e^x f^ (x) d x=

Options

  1. A1 2 [e^x f(x)-g(x) ]+C
  2. B1 2 [e^x f(x)+g(x) ]+C
  3. Ce^x f^ (x)+g(x) 2 +C
  4. D1 2 [e^x f(x)+e^x g(x) ]+C

Correct answer

A. 1 2 [e^x f(x)-g(x) ]+C

Step-by-step solution

We are given that aligned & e^x [f(x)-f^ (x) ] d x=g(x)+c & e^x f(x)- e^x f^ (x)=g(x)+c & e^x f(x) d x= e^x f^ (x)-g(x)+c & Now e^x f^ (x) d x= & f(x) e^x- f^ (x) e^x d x-g(x)+c & 2 e^x f^ (x) d x=e^x f(x)-g(x)+c & e^x f^ (x) d x= 1 2 [e^x f(x)-g(x) ]+c aligned

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