MCQ
$\int_0^{\pi /2} {\frac{{{{\sin }^{3/2}}x\,dx}}{{{{\cos }^{3/2}}x + {{\sin }^{3/2}}x}}} = $
- A$0$
- B$\pi $
- C$\pi /2$
- ✓$\pi /4$
$= \int_0^{\pi /2} {\frac{{{{\sin }^{3/2}}\left( {\frac{\pi }{2} - x} \right)}}{{{{\cos }^{3/2}}\left( {\frac{\pi }{2} - x} \right) + {{\sin }^{3/2}}\left( {\frac{\pi }{2} - x} \right)}}dx} $
$= \int_0^{\pi /2} {\frac{{{{\cos }^{3/2}}x\,dx}}{{{{\sin }^{3/2}}x + {{\cos }^{3/2}}x}}} $.....$(ii)$
Adding $(i)$ and $(ii),$ we get $I = \frac{1}{2}\int_0^{\pi /2} {1dx = \frac{1}{2}[x]_0^{\pi /2} = \frac{\pi }{4}} $.
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