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7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
$\int_{ - \pi /2}^{\pi /2} {{{\sin }^2}x\,dx = } $
  • A
    $\pi $
  • ✓
    $\frac{\pi }{2}$
  • C
    $\frac{\pi }{2} - \frac{1}{2}$
  • D
    $\pi - 1$
✓

Answer

Correct option: B.
$\frac{\pi }{2}$
b
(b)$\int_{ - \pi /2}^{\pi /2} {{{\sin }^2}x\,dx = 2\int_0^{\pi /2} {{{\sin }^2}x\,dx = 2\frac{{\Gamma \left( {\frac{3}{2}} \right).\Gamma \left( {\frac{1}{2}} \right)}}{{2\Gamma \left( {\frac{{2 + 2}}{2}} \right)}}} = \frac{\pi }{2}} $.

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