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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {{{\left( {\cos \frac{x}{2} - \sin \frac{x}{2}} \right)}^2}dx = } $
  • ✓
    $x + \cos x + c$
  • B
    $2{\cos ^2}\frac{x}{2} + c$
  • C
    $\frac{1}{3}{\left( {\cos \frac{x}{2} - \frac{x}{2}} \right)^3} + c$
  • D
    $x - \cos x + c$
✓

Answer

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

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