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JEE Main & Advanced Sample Paper JEE Main Sample Paper-45

  • question_answer
    Let \[[\cdot ]\]denotes the greatest integer function, then \[\int_{1}^{2}{[3\,x]}\] is equal to

    A)  4                                

    B)  5

    C)  6                                

    D)  7

    Correct Answer: A

    Solution :

     \[\int_{1}^{2}{[3x]\,dx=}\,\int_{1}^{1/3}{[3x]\,dx+}\,\int_{4/3}^{5/3}{[3x]\,dx}\] \[+\,\int_{5/3}^{2}{[3x]\,dx}\] \[=3\,\left( \frac{4}{3}-1 \right)+4\,\left( \frac{5}{3}-\frac{4}{3} \right)+5\,\left( 2-\frac{5}{3} \right)=4\]


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