A) \[{{\sin }^{2}}x+1\]
B) \[\sin {{x}^{2}}+{{x}^{2}}+1\]
C) \[\frac{{{\cos }^{3}}x}{3}-\cos x\]
D) \[\frac{1}{4}{{\sin }^{4}}x-\frac{3}{4}{{\sin }^{2}}x\]
Correct Answer: C
Solution :
\[\int_{{}}^{{}}{{{\sin }^{3}}x\,dx}=\int_{{}}^{{}}{{{\sin }^{2}}x\,.\,\sin x\,dx}\] \[=\int_{{}}^{{}}{\sin x(1-{{\cos }^{2}}x)\,dx}\] \[=\int_{{}}^{{}}{\sin x\,dx}-\int_{{}}^{{}}{{{\cos }^{2}}x\,.\,\sin x\,dx}\]\[=-\cos x+\frac{{{\cos }^{3}}x}{3}\].
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