2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Definite Integration

JEE Main & Advanced Mathematics Definite Integration Question Bank Properties of Definite Integration

  • question_answer
    If \[f(x)=\left\{ \begin{matrix}    4x+3\,, & \text{if} & 1\le x\le 2  \\    3x+5\,, & \text{if} & 2<x\le 4  \\ \end{matrix} \right.\] then \[\int_{1}^{4}{\,f(x)}\,dx=\]

    A)                 80          

    B)                 20

    C)                 \[-20\] 

    D)                 37

    Correct Answer: D

    Solution :

               \[\int_{1}^{4}{f(x)dx=\int_{1}^{2}{(4x+3)dx+\int_{2}^{4}{(3x+5)\,dx}}}\]                                                \[=\left| 2{{x}^{2}}+3x \right|_{1}^{2}+\left| \frac{3{{x}^{2}}}{2}+5x \right|_{2}^{4}=37\].


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