2. Sample Papers
  3. JEE Main & Advanced

JEE Main & Advanced Sample Paper JEE Main Sample Paper-2

  • question_answer
    \[{{l}_{m,\,n}}=\int_{{}}^{{}}{{{\sin }^{m}}x\cdot \,{{\cos }^{n}}xdx,}\] then \[{{l}_{m,\,n}}=c\,{{\sin }^{a}}x\,{{\cos }^{b}}x+\lambda {{l}_{\operatorname{m}-2,\,n+2}}\] then \[\lambda =\]

    A)  \[\frac{a}{b}\]                                 

    B)  \[ac\]

    C)  \[\frac{b}{a}\]                                 

    D)  None of these

    Correct Answer: A

    Solution :

    \[{{I}_{m,\,n}}=\int{{{\sin }^{m-1}}x\,\sin x\,{{\cos }^{n}}x\,dx}\] \[=\frac{-{{\sin }^{m-1}}x{{\cos }^{n+1}}x}{n+1}+\frac{m-1}{n+1}\int{{{\sin }^{m-2}}x{{\cos }^{n+2}}xdx}\] \[\Rightarrow \,\,c=\frac{-1}{n+1},\,a=m-1,\,b=n+1\] \[\lambda =\frac{m-1}{n+1}=\frac{a}{b}\]


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