RD Sharma - Mathematics (Volume 2)

Book: RD Sharma - Mathematics (Volume 2)

Chapter: 21. Areas of Bounded Regions

Subject: Maths - Class 12th

Q. No. 34 of Exercise 21.3

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34

Using integration find the area of the region {(x,y)|x – 1| y √5 – x2}.

To find area of region

{(x,y)|x – 1|y√5 – x2}


|x – 1| = y



And x2 + y2 = 5 …(iii)


|x – 1|y√5 – x2


|x – 1| = √5 – x2


X = 2, – 1


Equation (i) and (ii) represent straight lines and equation (iii) is a circle with centre (0,0), meets axes at (±√5,0) and (0,±√5).


These are shown in the graph below: -



Required area = Region BCDB + Region CADC









The area of the region {(x,y)|x – 1|y√s – x2} is


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