MCQ
$\int_0^{\pi /2} {{{\cos }^2}x\,dx = } $
- A$1 - \frac{\pi }{4}$
- B$1 + \frac{\pi }{4}$
- ✓$\frac{\pi }{4}$
- D$\frac{\pi }{2}$
✓
Answer
Correct option: C.
$\frac{\pi }{4}$
c
(c) Using gamma function,
(c) Using gamma function,
$\int_0^{\pi /2} {\,\,{{\cos }^2}x\,dx} $
$=\frac{{\Gamma \left( {\frac{3}{2}} \right)\Gamma \left( {\frac{1}{2}} \right)}}{{2\Gamma (2)}}$
$= \frac{{\frac{1}{2}\Gamma \left( {\frac{1}{2}} \right)\Gamma \left( {\frac{1}{2}} \right)}}{{2.1.\Gamma (1)}} = \frac{\pi }{4}$.
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