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

  • question_answer
    If \[P=\int_{0}^{3\pi }{f({{\cos }^{2}}x)dx}\,\,\text{and}\,\,Q=\int_{0}^{\pi }{f({{\cos }^{2}}x)dx}\], then                                                 [Orissa JEE 2004]

    A)                 \[P-Q=0\]           

    B)                 \[P-2Q=0\]

    C)                 \[P-3Q=0\]         

    D)                 \[P-5Q=0\]

    Correct Answer: C

    Solution :

               \[P=\int_{0}^{3\pi }{f({{\cos }^{2}}x)dx}\] and \[Q=\int_{0}^{\pi }{f({{\cos }^{2}}x)dx}\]                            Also, \[P=3\int_{0}^{\pi }{f({{\cos }^{2}}x)dx=3Q}\] Þ \[P-3Q=0\].


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