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STD 12 - 7.2 definite integral — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 7.2 definite integral4 Marks
MCQ
$\int_0^{\pi /2} {{{\sin }^2}x{{\cos }^3}x} \,dx = $
  • A
    $0$
  • ✓
    $\frac{2}{{15}}$
  • C
    $\frac{4}{{15}}$
  • D
    None of these
✓

Answer

Correct option: B.
$\frac{2}{{15}}$
b
(b) Using gamma function,

$\int_0^{\pi /2} {{{\sin }^2}x{{\cos }^3}xdx = \frac{{\Gamma \,\left( {\frac{3}{2}} \right)\,\Gamma 2}}{{2\Gamma \left( {\frac{7}{2}} \right)}} = \frac{2}{{15}}} $.

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