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

  • question_answer
    . The integral value \[\int_{-2}^{0}{\left[ {{x}^{3}}+3{{x}^{2}}+3x+3+(x+1)\cos (x+1) \right]\ dx}\] is           [IIT Screening 2005]

    A)                 2             

    B)                 4

    C)                 0             

    D)                 8             

    Correct Answer: B

    Solution :

               Let \[x+1=t\] when \[x=-2\to 0\], then \[t=-1\to 1\]                    \[I=\int_{-1}^{1}{({{t}^{3}}+2+t\cos t)\ dt}\]                    \[\ \text{Since}\ \,{{t}^{3}}\text{and }t\ \text{cos}\,\,t\] are odd functions                                 \[\therefore \]\[I=\int_{-1}^{1}{2dt=[2t]_{-1}^{1}=4}\].


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