The area (in sq.units) enclosed between the curve |x|+|y|<3 and x2−6x+y2<0 is
A
2π
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B
7π4
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C
3π
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D
9π4
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Solution
The correct option is D9π4 Given curve : |x|+|y|<3 and x2−6x+y2<0⇒(x−3)2+y2<9
The region bounded is shown as :
So, Required Area = Area of Arc ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯(CAOB) =θ360∘×(πR2)
Here, θ=π2(angle ACB),R=3(radius of arc) =π2⋅π(3)22π=9π4sq.units