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7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
$\int_0^\pi {{{\sin }^5}\left( {\frac{x}{2}} \right)\,dx} $ equals
  • ✓
    $\frac{{16}}{{15}}$
  • B
    $\frac{{32}}{{15}}$
  • C
    $\frac{8}{{15}}$
  • D
    $\frac{5}{6}$
✓

Answer

Correct option: A.
$\frac{{16}}{{15}}$
a
(a) $\int_0^\pi {{{\sin }^5}\frac{2}{x}dx = 2\int_0^{\pi /2} {{{\sin }^5}tdt = 2.\frac{{\Gamma \frac{6}{2}.\Gamma \frac{1}{2}}}{{2\Gamma \frac{7}{2}}} = \frac{{16}}{{15}}} } $.

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