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$3$
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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