A) \[\frac{\pi }{2}\]
B) \[\frac{\pi }{4}\]
C) \[\frac{\pi }{8}\]
D) 0
Correct Answer: D
Solution :
[d] Let \[f(x)=\frac{{{\sin }^{5}}x{{\cos }^{3}}x}{{{x}^{4}}}\] \[f(-x)=\frac{{{\sin }^{5}}(-x){{\cos }^{3}}(-x)}{{{(-x)}^{4}}}\] \[=\frac{-{{\sin }^{5}}x{{\cos }^{3}}x}{{{x}^{4}}}=-f(x)\] \[\Rightarrow f(x)\] is an odd function. Hence, \[\int\limits_{-\frac{\pi }{6}}^{\frac{\pi }{6}}{\frac{{{\sin }^{5}}x{{\cos }^{3}}x}{{{x}^{4}}}dx=0}\]
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