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

JEE Main & Advanced Mathematics Indefinite Integrals Question Bank Integration by Parts

  • question_answer
    If \[\int{x{{e}^{2x}}\,\,dx}\] is equal to \[{{e}^{2x}}f(x)+C\] where C is constant of integration, then f(x) is                 [UPSEAT 2001]

    A)                 \[(3x-1)/4\]

    B)                 \[(2x+1)/2\]

    C)                 \[(2x-1)/4\]

    D)                 \[(x-4)/6\]

    Correct Answer: C

    Solution :

                    \[\int{x{{e}^{2x}}dx=\frac{x{{e}^{2x}}}{2}}-\int{1.\,\frac{{{e}^{2x}}}{2}dx}\]\[=\frac{x{{e}^{2x}}}{2}-\frac{{{e}^{2x}}}{4}+c\]                                                   \[={{e}^{2x}}\left( \frac{2x-1}{4} \right)+c\] Þ \[f(x)=\frac{(2x-1)}{4}.\]


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