Cho ∫sin^n x.cosx dx =164 . Khi đó n bằng :

Question

Cho \(\int _{0}^{\frac{\pi }{6} }\sin ^{n} x\cos xdx=\frac{1}{64} \) . Khi đó n bằng :

\( A.3. \)                 

\(B.4.          \)            

\(C.6.     \)                   

\(D.5. \)

Answer 1

Chọn A 

Ta có  \(\int _{0}^{\frac{\pi }{6} }\sin ^{n} x\cos xdx= \int _{0}^{\frac{\pi }{6} }\sin ^{n} xd\sin x= \frac{\sin ^{n+1} x}{n+1} \left|\begin{array}{l} {\frac{\pi }{6} } \\ {0} \end{array}\right.\)

\(=\frac{\left(\frac{1}{2} \right)^{n+1} }{n+1}  \Rightarrow \frac{\left(\frac{1}{2} \right)^{n+1} }{n+1} =\frac{1}{64} \Leftrightarrow n=3.\)