Question

Area between the curve y = cos x and x- axis when 0 $\le$ x is [MP PET 1997]

• A. 2
• B. 4
• C. 3
• D. 0.0

Answer 1

The correct option is B

4

$y=cosx,Whenxϵ[0,\frac{\pi }{2}],cosx\ge 0$
$Whenxϵ[\frac{\pi }{2},\frac{3\pi }{2}],cosx\le 0$
$Whenxϵ[\frac{3\pi }{2},2\pi ],cosx\ge 0$
Thus required area is given by,
${\int }_0^{\frac{\pi }{2}}ydx={\int }_0^{\frac{\pi }{2}}cosxdx+{\int }_{\frac{\pi }{2}}^{\frac{3\pi }{2}}(-cosx)dx+{\int }_{\frac{3\pi }{2}}^{2\pi }cosxdx$
= 1 + 2 + 1 = 4sq.unit