A) \[\frac{3\pi }{2}x-\frac{{{x}^{2}}}{2}+C\]
B) \[\frac{\pi }{2}x-\frac{{{x}^{2}}}{2}+C\]
C) \[\frac{3\pi }{2}x+\frac{{{x}^{2}}}{2}+C\]
D) \[\frac{\pi }{2}x+\frac{{{x}^{3}}}{3}+C\]
E) None of these
Correct Answer: E
Solution :
Let \[l=\int{{{\sin }^{-1}}\,\cos \,3x\,dx}\] \[=\int{{{\sin }^{-1}}\sin \left( \frac{\pi }{2}-3x \right)}\,dx\] \[=\int{\left( \frac{\pi }{2}-3x \right)}\,dx\] \[=\frac{\pi }{2}x-\frac{3{{x}^{2}}}{2}+C\]
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