MCQ
Area between the curve $y = \cos x$ and $x - $ axis when $0 \le x \le 2\pi $ is
  • A
    $2$
  • $4$
  • C
    $0$
  • D
    $3$

Answer

Correct option: B.
$4$
b
(b) $y = \cos x$,

When $x \in \left[ {0,\frac{\pi }{2}} \right],\cos x \ge 0$

When $x \in \left[ {\frac{\pi }{2},\frac{{3\pi }}{2}} \right],\cos x \le 0$

When $x \in \left[ {\frac{{3\pi }}{2},2\pi } \right],\cos x \ge 0$

Thus required area is given by,

$\int_0^{\pi /2} {\,\,ydx} = \int_0^{\pi /2} {\cos x\,dx + \int_{\pi /2}^{3\pi /2} {( - \cos x)dx + \int_{3\pi /2}^{2\pi } {\,\cos xdx} } } $

$ = 1 + 2 + 1 = 4\,\, sq. \,unit$

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