_ ^ ( x 2 - x 2 ) ^2 dx = - Vidyadip

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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