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

  • question_answer
    If \[f(x)=\left\{ \begin{matrix}    {{e}^{\cos x}}\sin x, & |x|\,\le 2  \\    2, & \text{otherwise}  \\ \end{matrix} \right.\], then \[\int_{\,-\,2}^{\,3}{f(x)\,dx}\] is equal to                                                    [IIT Screening 2000]

    A)                 0             

    B)                 1

    C)                 2             

    D)                 3

    Correct Answer: C

    Solution :

               \[\int_{-2}^{3}{f(x)\,dx=}\int_{-2}^{2}{f(x)\,dx+\int_{2}^{3}{\,f(x)\,dx}}\]                    \[\because \] \[{{e}^{\cos x}}\sin x\]is an odd function                 \[\therefore \,\int_{-2}^{3}{f(x)\,dx}=\int_{-2}^{2}{{{e}^{\cos x}}\sin x\,dx+\int_{2}^{3}{2\,dx=0+2\,(3-2)=2}}\].


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