JEE Main & Advanced JEE Main Paper (Held on 09-4-2019 Morning)

  • question_answer The value of\[\int\limits_{0}^{\pi /2}{\frac{{{\sin }^{3}}x}{\sin x+\cos x}}dx\]is [JEE Main 9-4-2019 Morning]

    A) \[\frac{\pi -2}{4}\]                 

    B) \[\frac{\pi -2}{8}\]

    C) \[\frac{\pi -1}{4}\]     

    D) \[\frac{\pi -1}{2}\]

    Correct Answer: C

    Solution :

                \[I=\int\limits_{0}^{\pi /2}{\frac{{{\sin }^{3}}x}{\sin x+\cos x}}dx\]           \[\Rightarrow \]\[I=\int\limits_{0}^{\pi /4}{\frac{{{\sin }^{3}}x+{{\cos }^{3}}x}{\sin x+\cos x}}dx\]           \[=\int\limits_{0}^{\pi /4}{(1-sin\,x\,cos\,x)\,}dx\]           \[=\left( x-\frac{{{\sin }^{2}}x}{2} \right)_{0}^{\pi /4}\]           \[=\frac{\pi }{4}-\frac{1}{4}\]               \[=\frac{\pi -1}{4}\]


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