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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {{{\sin }^{ - 1}}} (\cos x)dx = $
  • A
    $\frac{{\pi x}}{2}$
  • B
    $\frac{{\pi {x^2}}}{2}$
  • ✓
    $\frac{{\pi x - {x^2}}}{2}$
  • D
    $\frac{{\pi x + {x^2}}}{2}$
✓

Answer

Correct option: C.
$\frac{{\pi x - {x^2}}}{2}$
c
(c) $\int_{}^{} {{{\sin }^{ - 1}}(\cos x)\,dx} = \int_{}^{} {\left\{ {\frac{\pi }{2} - {{\cos }^{ - 1}}(\cos x)} \right\}} \,dx$
$ = \frac{\pi }{2}x - \frac{{{x^2}}}{2} = \frac{{\pi x - {x^2}}}{2}$.

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