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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2008

  • question_answer
    The value of \[\int_{-2}^{2}{(a{{x}^{3}}+bx+c)}dx\] depends on the

    A)  value of b

    B)  value of c

    C)  value of a

    D)  values of a and b

    Correct Answer: B

    Solution :

    Let \[I=\int_{-2}^{2}{(a{{x}^{3}}+bx+c)dx}\] We know,\[\int_{-a}^{a}{f(x)dx=\left\{ \begin{matrix}    2\int_{0}^{a}{f(x)\,dx,} & if & f(-x)=f(x)  \\    0, & if & f(-x)=-f(x)  \\ \end{matrix} \right.}\] In the given integral, \[a{{x}^{3}}\]and bx are odd functions. Hence, it depends only on the value of c.


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