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Find the area bounded by y=| sin x -(1)/...

Find the area bounded by `y=| sin x -(1)/(2)| and y= 1" for "x in [0,pi]`

Text Solution

Verified by Experts

The correct Answer is:
`((pi)/(2)+2)`sq. units
`y=|sin x-(1)/(2)|={{:((1)/(2)-sin x",",0lexle(pi)/(6)),(sin x-(1)/(2)",",(pi)/(6)ltxlt(5pi)/(6)),((1)/(2)-sin x",",(5pi)/(6)lexlepi):}`

`therefore" Required area is "`
`A=pi-2(overset((pi)/(2))underset(0)int((1)/(2)-sin x)dx +overset((pi)/(2))underset(0)int(sin x-(1)/(2))dx)`
`pi-2((1)/(2)x + cos x)_(0)^(pi//6)+2(-cos x-(1)/(2))_(pi//6)^(pi//2)`
`=(pi)/(2)+2`
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