2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Indefinite Integrals

JEE Main & Advanced Mathematics Indefinite Integrals Question Bank Self Evaluation Test - Integrals

  • question_answer
    If \[\int{g(x)dx=g(x),}\] then\[\int{g(x)\{f(x)+f'(x)\}dx}\] is equal to

    A) \[g(x)f(x)-g(x)f'(x)+C\]

    B) \[g(x)f'(x)+C\]

    C) \[g(x)f(x)+C\]

    D) \[g(x){{f}^{2}}(x)+C\]

    Correct Answer: C

    Solution :

    [c] \[\int{g(x)\{f(x)+f'(x)\}dx}\] \[=\int{g(x)f(x)dx+\int{g(x)f'(x)dx}}\] \[=f(x)\int{g(x)dx-\int{\{f'(x)g(x)dx\}dx+\int{g(x)f'(x)dx}}}\] \[=f(x)g(x)-\int{f'(x)g(x)dx+\int{g(x)f'(x)dx}}\] [Given \[\int{g(x)dx=g(x)}\]] \[=f(x)g(x)+c\]


You need to login to perform this action.
You will be redirected in 3 sec spinner